LMFDB - Space of Modular Forms of Level 9450, Weight 2, and Trivial Character

Defining parameters

Level:	$ N $	=	$ 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	=	$ 2 $
Character orbit:	$[\chi]$	=	9450.a (trivial)
Character field:			$\Q$
Newforms:			$ 128 $
Sturm bound:			$4320$
Trace bound:			$17$
Distinguishing $T_p$:			$11$, $13$, $17$, $19$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(9450))$.

	Total	New	Old
Modular forms	2232	152	2080
Cusp forms	2089	152	1937
Eisenstein series	143	0	143

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$2$	$3$	$5$	$7$	Fricke	Dim.
$+$	$+$	$+$	$+$	$+$	$8$
$+$	$+$	$+$	$-$	$-$	$10$
$+$	$+$	$-$	$+$	$-$	$10$
$+$	$+$	$-$	$-$	$+$	$10$
$+$	$-$	$+$	$+$	$-$	$10$
$+$	$-$	$+$	$-$	$+$	$8$
$+$	$-$	$-$	$+$	$+$	$10$
$+$	$-$	$-$	$-$	$-$	$10$
$-$	$+$	$+$	$+$	$-$	$11$
$-$	$+$	$+$	$-$	$+$	$7$
$-$	$+$	$-$	$+$	$+$	$8$
$-$	$+$	$-$	$-$	$-$	$12$
$-$	$-$	$+$	$+$	$+$	$7$
$-$	$-$	$+$	$-$	$-$	$11$
$-$	$-$	$-$	$+$	$-$	$12$
$-$	$-$	$-$	$-$	$+$	$8$
Plus space				$+$	$66$
Minus space				$-$	$86$

Trace form

$152q $ $\mathstrut +\mathstrut 152q^{4} $ $\mathstrut +\mathstrut O(q^{10}) $

$152q $ $\mathstrut +\mathstrut 152q^{4} $ $\mathstrut -\mathstrut 8q^{13} $ $\mathstrut +\mathstrut 152q^{16} $ $\mathstrut +\mathstrut 8q^{19} $ $\mathstrut +\mathstrut 4q^{22} $ $\mathstrut -\mathstrut 8q^{34} $ $\mathstrut -\mathstrut 20q^{37} $ $\mathstrut -\mathstrut 4q^{43} $ $\mathstrut +\mathstrut 8q^{46} $ $\mathstrut +\mathstrut 152q^{49} $ $\mathstrut -\mathstrut 8q^{52} $ $\mathstrut -\mathstrut 28q^{58} $ $\mathstrut -\mathstrut 16q^{61} $ $\mathstrut +\mathstrut 152q^{64} $ $\mathstrut +\mathstrut 12q^{67} $ $\mathstrut -\mathstrut 24q^{73} $ $\mathstrut +\mathstrut 8q^{76} $ $\mathstrut +\mathstrut 8q^{79} $ $\mathstrut -\mathstrut 32q^{82} $ $\mathstrut +\mathstrut 4q^{88} $ $\mathstrut -\mathstrut 4q^{91} $ $\mathstrut -\mathstrut 8q^{94} $ $\mathstrut +\mathstrut 48q^{97} $ $\mathstrut +\mathstrut O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(9450))$ into irreducible Hecke orbits

Label	Dim.	$A$	Field	CM	Traces				A-L signs				$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	2	3	5	7	$q$-expansion
9450.2.a.a	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}-2q^{13}+\cdots$
9450.2.a.b	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}+q^{13}+\cdots$
9450.2.a.c	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{11}-5q^{13}+\cdots$
9450.2.a.d	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{11}+q^{13}+\cdots$
9450.2.a.e	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-5q^{13}+\cdots$
9450.2.a.f	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-q^{13}+\cdots$
9450.2.a.g	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+q^{13}+\cdots$
9450.2.a.h	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+4q^{13}+\cdots$
9450.2.a.i	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+5q^{13}+\cdots$
9450.2.a.j	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{11}+5q^{13}+\cdots$
9450.2.a.k	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-q^{11}+3q^{13}+\cdots$
9450.2.a.l	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{13}+q^{14}+\cdots$
9450.2.a.m	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{13}+q^{14}+\cdots$
9450.2.a.n	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{13}+q^{14}+\cdots$
9450.2.a.o	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{13}+q^{14}+\cdots$
9450.2.a.p	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+7q^{13}+q^{14}+\cdots$
9450.2.a.q	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}-5q^{13}+\cdots$
9450.2.a.r	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}+5q^{13}+\cdots$
9450.2.a.s	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}-5q^{13}+\cdots$
9450.2.a.t	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}+6q^{13}+\cdots$
9450.2.a.u	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}-5q^{13}+\cdots$
9450.2.a.v	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}+q^{13}+\cdots$
9450.2.a.w	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{11}-6q^{13}+\cdots$
9450.2.a.x	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{11}-q^{13}+\cdots$
9450.2.a.y	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}-5q^{13}+\cdots$
9450.2.a.z	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$-1$	$+$	$+$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}+4q^{13}+\cdots$
9450.2.a.ba	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}+5q^{13}+\cdots$
9450.2.a.bb	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-5q^{11}+5q^{13}+\cdots$
9450.2.a.bc	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}-3q^{13}+\cdots$
9450.2.a.bd	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}+q^{13}+\cdots$
9450.2.a.be	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}+6q^{13}+\cdots$
9450.2.a.bf	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}-6q^{13}+\cdots$
9450.2.a.bg	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}-q^{14}+\cdots$
9450.2.a.bh	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+3q^{13}+\cdots$
9450.2.a.bi	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+5q^{13}+\cdots$
9450.2.a.bj	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-q^{11}-5q^{13}+\cdots$
9450.2.a.bk	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-q^{11}+5q^{13}+\cdots$
9450.2.a.bl	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-7q^{13}-q^{14}+\cdots$
9450.2.a.bm	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{13}-q^{14}+\cdots$
9450.2.a.bn	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-q^{13}-q^{14}+\cdots$
9450.2.a.bo	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{13}-q^{14}+\cdots$
9450.2.a.bp	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}-3q^{13}+\cdots$
9450.2.a.bq	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}-3q^{13}+\cdots$
9450.2.a.br	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}+3q^{13}+\cdots$
9450.2.a.bs	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{11}-4q^{13}+\cdots$
9450.2.a.bt	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-5q^{13}+\cdots$
9450.2.a.bu	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-q^{13}+\cdots$
9450.2.a.bv	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}+q^{13}+\cdots$
9450.2.a.bw	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}-q^{13}+\cdots$
9450.2.a.bx	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}-q^{14}+\cdots$
9450.2.a.by	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}+5q^{13}+\cdots$
9450.2.a.bz	$1$	$75.459$	$\Q$	None	$-1$	$0$	$0$	$1$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+6q^{11}+2q^{13}+\cdots$
9450.2.a.ca	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}-5q^{13}+\cdots$
9450.2.a.cb	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}+4q^{13}+\cdots$
9450.2.a.cc	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}-6q^{13}+\cdots$
9450.2.a.cd	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}-q^{13}+\cdots$
9450.2.a.ce	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}-5q^{13}+\cdots$
9450.2.a.cf	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}+q^{13}+\cdots$
9450.2.a.cg	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}-5q^{13}+\cdots$
9450.2.a.ch	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}+6q^{13}+\cdots$
9450.2.a.ci	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-q^{11}-5q^{13}+\cdots$
9450.2.a.cj	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-q^{11}+5q^{13}+\cdots$
9450.2.a.ck	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-5q^{13}-q^{14}+\cdots$
9450.2.a.cl	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-5q^{13}-q^{14}+\cdots$
9450.2.a.cm	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots$
9450.2.a.cn	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{13}-q^{14}+\cdots$
9450.2.a.co	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+7q^{13}-q^{14}+\cdots$
9450.2.a.cp	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{11}+3q^{13}+\cdots$
9450.2.a.cq	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}+5q^{13}+\cdots$
9450.2.a.cr	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}-5q^{13}+\cdots$
9450.2.a.cs	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}-q^{13}+\cdots$
9450.2.a.ct	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+q^{13}+\cdots$
9450.2.a.cu	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+4q^{13}+\cdots$
9450.2.a.cv	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+5q^{13}+\cdots$
9450.2.a.cw	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+5q^{11}-5q^{13}+\cdots$
9450.2.a.cx	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+5q^{11}+q^{13}+\cdots$
9450.2.a.cy	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}-2q^{13}+\cdots$
9450.2.a.cz	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$-1$	$-$	$+$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}+q^{13}+\cdots$
9450.2.a.da	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}+2q^{13}+\cdots$
9450.2.a.db	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}-q^{13}+\cdots$
9450.2.a.dc	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}+q^{14}+\cdots$
9450.2.a.dd	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}+5q^{13}+\cdots$
9450.2.a.de	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}-5q^{13}+\cdots$
9450.2.a.df	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}-q^{13}+\cdots$
9450.2.a.dg	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}+q^{13}+\cdots$
9450.2.a.dh	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{11}-4q^{13}+\cdots$
9450.2.a.di	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}-3q^{13}+\cdots$
9450.2.a.dj	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}-3q^{13}+\cdots$
9450.2.a.dk	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}+3q^{13}+\cdots$
9450.2.a.dl	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-7q^{13}+q^{14}+\cdots$
9450.2.a.dm	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{13}+q^{14}+\cdots$
9450.2.a.dn	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots$
9450.2.a.do	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{13}+q^{14}+\cdots$
9450.2.a.dp	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}-5q^{13}+\cdots$
9450.2.a.dq	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}+5q^{13}+\cdots$
9450.2.a.dr	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}-6q^{13}+\cdots$
9450.2.a.ds	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+q^{14}+\cdots$
9450.2.a.dt	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+3q^{13}+\cdots$
9450.2.a.du	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+5q^{13}+\cdots$
9450.2.a.dv	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}-3q^{13}+\cdots$
9450.2.a.dw	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}+q^{13}+\cdots$
9450.2.a.dx	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}+6q^{13}+\cdots$
9450.2.a.dy	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}+5q^{13}+\cdots$
9450.2.a.dz	$1$	$75.459$	$\Q$	None	$1$	$0$	$0$	$1$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+6q^{11}+5q^{13}+\cdots$
9450.2.a.ea	$2$	$75.459$	$\Q(\sqrt{6}) $	None	$-2$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots$
9450.2.a.eb	$2$	$75.459$	$\Q(\sqrt{3}) $	None	$-2$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(2+\cdots)q^{13}+\cdots$
9450.2.a.ec	$2$	$75.459$	$\Q(\sqrt{7}) $	None	$-2$	$0$	$0$	$-2$	$+$	$-$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots$
9450.2.a.ed	$2$	$75.459$	$\Q(\sqrt{73}) $	None	$-2$	$0$	$0$	$-2$	$+$	$-$	$+$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9450.2.a.ee	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$-2$	$0$	$0$	$-2$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}+(-1+\cdots)q^{13}+\cdots$
9450.2.a.ef	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$-2$	$0$	$0$	$-2$	$+$	$+$	$-$	$+$	$q-q^{2}+q^{4}-q^{7}-q^{8}+(2+\beta )q^{11}+\cdots$
9450.2.a.eg	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$-2$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+(-2+\beta )q^{11}+\cdots$
9450.2.a.eh	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$-2$	$0$	$0$	$2$	$+$	$-$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+(1+\cdots)q^{13}+\cdots$
9450.2.a.ei	$2$	$75.459$	$\Q(\sqrt{3}) $	None	$-2$	$0$	$0$	$2$	$+$	$+$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9450.2.a.ej	$2$	$75.459$	$\Q(\sqrt{7}) $	None	$-2$	$0$	$0$	$2$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9450.2.a.ek	$2$	$75.459$	$\Q(\sqrt{6}) $	None	$-2$	$0$	$0$	$2$	$+$	$-$	$-$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+\beta q^{11}+(1+\cdots)q^{13}+\cdots$
9450.2.a.el	$2$	$75.459$	$\Q(\sqrt{97}) $	None	$-2$	$0$	$0$	$2$	$+$	$+$	$+$	$-$	$q-q^{2}+q^{4}+q^{7}-q^{8}+(1+\beta )q^{11}+\cdots$
9450.2.a.em	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$2$	$0$	$0$	$-2$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}+(-1+\cdots)q^{13}+\cdots$
9450.2.a.en	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$2$	$0$	$0$	$-2$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+(-2+\beta )q^{11}+\cdots$
9450.2.a.eo	$2$	$75.459$	$\Q(\sqrt{73}) $	None	$2$	$0$	$0$	$-2$	$-$	$-$	$+$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9450.2.a.ep	$2$	$75.459$	$\Q(\sqrt{6}) $	None	$2$	$0$	$0$	$-2$	$-$	$+$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots$
9450.2.a.eq	$2$	$75.459$	$\Q(\sqrt{7}) $	None	$2$	$0$	$0$	$-2$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots$
9450.2.a.er	$2$	$75.459$	$\Q(\sqrt{3}) $	None	$2$	$0$	$0$	$-2$	$-$	$-$	$-$	$+$	$q+q^{2}+q^{4}-q^{7}+q^{8}+\beta q^{11}+(2+\cdots)q^{13}+\cdots$
9450.2.a.es	$2$	$75.459$	$\Q(\sqrt{97}) $	None	$2$	$0$	$0$	$2$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+(-1-\beta )q^{11}+\cdots$
9450.2.a.et	$2$	$75.459$	$\Q(\sqrt{7}) $	None	$2$	$0$	$0$	$2$	$-$	$+$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9450.2.a.eu	$2$	$75.459$	$\Q(\sqrt{3}) $	None	$2$	$0$	$0$	$2$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots$
9450.2.a.ev	$2$	$75.459$	$\Q(\sqrt{6}) $	None	$2$	$0$	$0$	$2$	$-$	$+$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+\beta q^{11}+(1+\cdots)q^{13}+\cdots$
9450.2.a.ew	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$2$	$0$	$0$	$2$	$-$	$-$	$-$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+(2+\beta )q^{11}+\cdots$
9450.2.a.ex	$2$	$75.459$	$\Q(\sqrt{10}) $	None	$2$	$0$	$0$	$2$	$-$	$-$	$+$	$-$	$q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+(1+\cdots)q^{13}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(9450))$ into lower level spaces

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Character orbit:	\([\chi]\)	=	9450.a (trivial)
Character field:			\(\Q\)
Newforms:			\( 128 \)
Sturm bound:			\(4320\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\)

\(2\)	\(3\)	\(5\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(8\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(10\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(10\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(10\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(10\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(8\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(10\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(10\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(11\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(7\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(8\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(7\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(11\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(8\)
Plus space				\(+\)	\(66\)
Minus space				\(-\)	\(86\)

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs				$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	2	3	5	7	$q$-expansion
9450.2.a.a	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}-2q^{13}+\cdots\)
9450.2.a.b	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}+q^{13}+\cdots\)
9450.2.a.c	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{11}-5q^{13}+\cdots\)
9450.2.a.d	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{11}+q^{13}+\cdots\)
9450.2.a.e	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-5q^{13}+\cdots\)
9450.2.a.f	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}-q^{13}+\cdots\)
9450.2.a.g	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+q^{13}+\cdots\)
9450.2.a.h	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+4q^{13}+\cdots\)
9450.2.a.i	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-3q^{11}+5q^{13}+\cdots\)
9450.2.a.j	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{11}+5q^{13}+\cdots\)
9450.2.a.k	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{11}+3q^{13}+\cdots\)
9450.2.a.l	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{13}+q^{14}+\cdots\)
9450.2.a.m	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}-5q^{13}+q^{14}+\cdots\)
9450.2.a.n	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{13}+q^{14}+\cdots\)
9450.2.a.o	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{13}+q^{14}+\cdots\)
9450.2.a.p	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+7q^{13}+q^{14}+\cdots\)
9450.2.a.q	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}-5q^{13}+\cdots\)
9450.2.a.r	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{11}+5q^{13}+\cdots\)
9450.2.a.s	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}-5q^{13}+\cdots\)
9450.2.a.t	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}+6q^{13}+\cdots\)
9450.2.a.u	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}-5q^{13}+\cdots\)
9450.2.a.v	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+3q^{11}+q^{13}+\cdots\)
9450.2.a.w	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{11}-6q^{13}+\cdots\)
9450.2.a.x	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{11}-q^{13}+\cdots\)
9450.2.a.y	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}-5q^{13}+\cdots\)
9450.2.a.z	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}+4q^{13}+\cdots\)
9450.2.a.ba	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}+5q^{13}+\cdots\)
9450.2.a.bb	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-5q^{11}+5q^{13}+\cdots\)
9450.2.a.bc	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}-3q^{13}+\cdots\)
9450.2.a.bd	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}+q^{13}+\cdots\)
9450.2.a.be	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-4q^{11}+6q^{13}+\cdots\)
9450.2.a.bf	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}-6q^{13}+\cdots\)
9450.2.a.bg	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}-q^{14}+\cdots\)
9450.2.a.bh	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+3q^{13}+\cdots\)
9450.2.a.bi	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+5q^{13}+\cdots\)
9450.2.a.bj	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{11}-5q^{13}+\cdots\)
9450.2.a.bk	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{11}+5q^{13}+\cdots\)
9450.2.a.bl	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-7q^{13}-q^{14}+\cdots\)
9450.2.a.bm	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{13}-q^{14}+\cdots\)
9450.2.a.bn	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{13}-q^{14}+\cdots\)
9450.2.a.bo	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{13}-q^{14}+\cdots\)
9450.2.a.bp	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}-3q^{13}+\cdots\)
9450.2.a.bq	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}-3q^{13}+\cdots\)
9450.2.a.br	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}+3q^{13}+\cdots\)
9450.2.a.bs	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{11}-4q^{13}+\cdots\)
9450.2.a.bt	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-5q^{13}+\cdots\)
9450.2.a.bu	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}-q^{13}+\cdots\)
9450.2.a.bv	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+3q^{11}+q^{13}+\cdots\)
9450.2.a.bw	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}-q^{13}+\cdots\)
9450.2.a.bx	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}-q^{14}+\cdots\)
9450.2.a.by	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+5q^{11}+5q^{13}+\cdots\)
9450.2.a.bz	\(1\)	\(75.459\)	\(\Q\)	None	\(-1\)	\(0\)	\(0\)	\(1\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+6q^{11}+2q^{13}+\cdots\)
9450.2.a.ca	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}-5q^{13}+\cdots\)
9450.2.a.cb	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}+4q^{13}+\cdots\)
9450.2.a.cc	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}-6q^{13}+\cdots\)
9450.2.a.cd	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}-q^{13}+\cdots\)
9450.2.a.ce	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}-5q^{13}+\cdots\)
9450.2.a.cf	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}+q^{13}+\cdots\)
9450.2.a.cg	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}-5q^{13}+\cdots\)
9450.2.a.ch	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}+6q^{13}+\cdots\)
9450.2.a.ci	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{11}-5q^{13}+\cdots\)
9450.2.a.cj	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-q^{11}+5q^{13}+\cdots\)
9450.2.a.ck	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-5q^{13}-q^{14}+\cdots\)
9450.2.a.cl	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-5q^{13}-q^{14}+\cdots\)
9450.2.a.cm	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots\)
9450.2.a.cn	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{13}-q^{14}+\cdots\)
9450.2.a.co	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+7q^{13}-q^{14}+\cdots\)
9450.2.a.cp	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{11}+3q^{13}+\cdots\)
9450.2.a.cq	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}+5q^{13}+\cdots\)
9450.2.a.cr	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}-5q^{13}+\cdots\)
9450.2.a.cs	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}-q^{13}+\cdots\)
9450.2.a.ct	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+q^{13}+\cdots\)
9450.2.a.cu	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+4q^{13}+\cdots\)
9450.2.a.cv	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+3q^{11}+5q^{13}+\cdots\)
9450.2.a.cw	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+5q^{11}-5q^{13}+\cdots\)
9450.2.a.cx	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+5q^{11}+q^{13}+\cdots\)
9450.2.a.cy	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}-2q^{13}+\cdots\)
9450.2.a.cz	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+6q^{11}+q^{13}+\cdots\)
9450.2.a.da	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}+2q^{13}+\cdots\)
9450.2.a.db	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}-q^{13}+\cdots\)
9450.2.a.dc	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}+q^{14}+\cdots\)
9450.2.a.dd	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-5q^{11}+5q^{13}+\cdots\)
9450.2.a.de	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}-5q^{13}+\cdots\)
9450.2.a.df	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}-q^{13}+\cdots\)
9450.2.a.dg	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-3q^{11}+q^{13}+\cdots\)
9450.2.a.dh	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{11}-4q^{13}+\cdots\)
9450.2.a.di	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}-3q^{13}+\cdots\)
9450.2.a.dj	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}-3q^{13}+\cdots\)
9450.2.a.dk	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{11}+3q^{13}+\cdots\)
9450.2.a.dl	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-7q^{13}+q^{14}+\cdots\)
9450.2.a.dm	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{13}+q^{14}+\cdots\)
9450.2.a.dn	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots\)
9450.2.a.do	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{13}+q^{14}+\cdots\)
9450.2.a.dp	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}-5q^{13}+\cdots\)
9450.2.a.dq	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+q^{11}+5q^{13}+\cdots\)
9450.2.a.dr	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}-6q^{13}+\cdots\)
9450.2.a.ds	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+q^{14}+\cdots\)
9450.2.a.dt	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+3q^{13}+\cdots\)
9450.2.a.du	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+5q^{13}+\cdots\)
9450.2.a.dv	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}-3q^{13}+\cdots\)
9450.2.a.dw	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}+q^{13}+\cdots\)
9450.2.a.dx	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}+6q^{13}+\cdots\)
9450.2.a.dy	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}+5q^{13}+\cdots\)
9450.2.a.dz	\(1\)	\(75.459\)	\(\Q\)	None	\(1\)	\(0\)	\(0\)	\(1\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+6q^{11}+5q^{13}+\cdots\)
9450.2.a.ea	\(2\)	\(75.459\)	\(\Q(\sqrt{6}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9450.2.a.eb	\(2\)	\(75.459\)	\(\Q(\sqrt{3}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
9450.2.a.ec	\(2\)	\(75.459\)	\(\Q(\sqrt{7}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
9450.2.a.ed	\(2\)	\(75.459\)	\(\Q(\sqrt{73}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ee	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+2q^{11}+(-1+\cdots)q^{13}+\cdots\)
9450.2.a.ef	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(-2\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(+\)	\(-\)	\(+\)	\(q-q^{2}+q^{4}-q^{7}-q^{8}+(2+\beta )q^{11}+\cdots\)
9450.2.a.eg	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+(-2+\beta )q^{11}+\cdots\)
9450.2.a.eh	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}+(1+\cdots)q^{13}+\cdots\)
9450.2.a.ei	\(2\)	\(75.459\)	\(\Q(\sqrt{3}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(+\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ej	\(2\)	\(75.459\)	\(\Q(\sqrt{7}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ek	\(2\)	\(75.459\)	\(\Q(\sqrt{6}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(-\)	\(-\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9450.2.a.el	\(2\)	\(75.459\)	\(\Q(\sqrt{97}) \)	None	\(-2\)	\(0\)	\(0\)	\(2\)	\(+\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}+q^{4}+q^{7}-q^{8}+(1+\beta )q^{11}+\cdots\)
9450.2.a.em	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}+(-1+\cdots)q^{13}+\cdots\)
9450.2.a.en	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+(-2+\beta )q^{11}+\cdots\)
9450.2.a.eo	\(2\)	\(75.459\)	\(\Q(\sqrt{73}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ep	\(2\)	\(75.459\)	\(\Q(\sqrt{6}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+\beta q^{11}+(-1+\cdots)q^{13}+\cdots\)
9450.2.a.eq	\(2\)	\(75.459\)	\(\Q(\sqrt{7}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
9450.2.a.er	\(2\)	\(75.459\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(+\)	\(q+q^{2}+q^{4}-q^{7}+q^{8}+\beta q^{11}+(2+\cdots)q^{13}+\cdots\)
9450.2.a.es	\(2\)	\(75.459\)	\(\Q(\sqrt{97}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+(-1-\beta )q^{11}+\cdots\)
9450.2.a.et	\(2\)	\(75.459\)	\(\Q(\sqrt{7}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(+\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.eu	\(2\)	\(75.459\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
9450.2.a.ev	\(2\)	\(75.459\)	\(\Q(\sqrt{6}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+\beta q^{11}+(1+\cdots)q^{13}+\cdots\)
9450.2.a.ew	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+(2+\beta )q^{11}+\cdots\)
9450.2.a.ex	\(2\)	\(75.459\)	\(\Q(\sqrt{10}) \)	None	\(2\)	\(0\)	\(0\)	\(2\)	\(-\)	\(-\)	\(+\)	\(-\)	\(q+q^{2}+q^{4}+q^{7}+q^{8}+2q^{11}+(1+\cdots)q^{13}+\cdots\)

Introduction and more

L-functions

Modular Forms

Varieties

Fields

Representations

Groups

Knowledge

Properties

Related objects

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Learn more about

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9450))\) into irreducible Hecke orbits

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9450))\) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	9450.2.a

Level	9450
Weight	2
Character orbit	a
Rep. character	\(\chi_{9450}(1,\cdot)\)
Character field	\(\Q\)
Dimension	152
Newforms	128
Sturm bound	4320
Trace bound	17