LMFDB - Space of modular forms of level 9408, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 9408 = 2^{6} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9408.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 118 $
Sturm bound:			$3584$
Trace bound:			$19$
Distinguishing $T_p$:			$5$, $11$, $13$, $17$, $19$, $31$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(9408))$.

	Total	New	Old
Modular forms	1888	164	1724
Cusp forms	1697	164	1533
Eisenstein series	191	0	191

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

$2$	$3$	$7$	Fricke	Dim.
$+$	$+$	$+$	$+$	$21$
$+$	$+$	$-$	$-$	$21$
$+$	$-$	$+$	$-$	$23$
$+$	$-$	$-$	$+$	$18$
$-$	$+$	$+$	$-$	$19$
$-$	$+$	$-$	$+$	$21$
$-$	$-$	$+$	$+$	$17$
$-$	$-$	$-$	$-$	$24$
Plus space			$+$	$77$
Minus space			$-$	$87$

Trace form

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(9408))$ into newform subspaces

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	7	$q$-expansion
9408.2.a.a	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-4$	$0$	$-$	$+$	$-$	$q-q^{3}-4q^{5}+q^{9}-6q^{11}+5q^{13}+\cdots$
9408.2.a.b	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-4$	$0$	$-$	$+$	$-$	$q-q^{3}-4q^{5}+q^{9}-4q^{11}-4q^{13}+\cdots$
9408.2.a.c	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-4$	$0$	$+$	$+$	$-$	$q-q^{3}-4q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots$
9408.2.a.d	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-3$	$0$	$+$	$+$	$+$	$q-q^{3}-3q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots$
9408.2.a.e	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-3$	$0$	$-$	$+$	$+$	$q-q^{3}-3q^{5}+q^{9}+q^{11}+4q^{13}+\cdots$
9408.2.a.f	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$-$	$+$	$+$	$q-q^{3}-2q^{5}+q^{9}-6q^{11}+3q^{13}+\cdots$
9408.2.a.g	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots$
9408.2.a.h	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$+$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
9408.2.a.i	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$+$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}-2q^{11}-3q^{13}+\cdots$
9408.2.a.j	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$+$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots$
9408.2.a.k	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}-2q^{11}+q^{13}+\cdots$
9408.2.a.l	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$+$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots$
9408.2.a.m	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$-$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
9408.2.a.n	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-2$	$0$	$+$	$+$	$-$	$q-q^{3}-2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots$
9408.2.a.o	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$q-q^{3}-q^{5}+q^{9}+q^{11}+q^{15}-8q^{17}+\cdots$
9408.2.a.p	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-1$	$0$	$-$	$+$	$-$	$q-q^{3}-q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots$
9408.2.a.q	$1$	$75.123$	$\Q$	None	$0$	$-1$	$-1$	$0$	$-$	$+$	$+$	$q-q^{3}-q^{5}+q^{9}+5q^{11}+q^{15}-4q^{17}+\cdots$
9408.2.a.r	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}-6q^{11}+2q^{13}+4q^{19}+\cdots$
9408.2.a.s	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$+$	$q-q^{3}+q^{9}-2q^{11}-5q^{13}-2q^{17}+\cdots$
9408.2.a.t	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$+$	$q-q^{3}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots$
9408.2.a.u	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$q-q^{3}+q^{9}-4q^{13}+4q^{17}+4q^{19}+\cdots$
9408.2.a.v	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}+4q^{13}-4q^{17}+4q^{19}+\cdots$
9408.2.a.w	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$q-q^{3}+q^{9}+2q^{11}-2q^{13}-4q^{17}+\cdots$
9408.2.a.x	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$+$	$+$	$-$	$q-q^{3}+q^{9}+2q^{11}+q^{13}+2q^{17}+\cdots$
9408.2.a.y	$1$	$75.123$	$\Q$	None	$0$	$-1$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}+2q^{11}+5q^{13}+2q^{17}+\cdots$
9408.2.a.z	$1$	$75.123$	$\Q$	None	$0$	$-1$	$1$	$0$	$+$	$+$	$-$	$q-q^{3}+q^{5}+q^{9}-5q^{11}-q^{15}+4q^{17}+\cdots$
9408.2.a.ba	$1$	$75.123$	$\Q$	None	$0$	$-1$	$1$	$0$	$+$	$+$	$+$	$q-q^{3}+q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots$
9408.2.a.bb	$1$	$75.123$	$\Q$	None	$0$	$-1$	$1$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{5}+q^{9}-q^{11}-q^{15}+8q^{17}+\cdots$
9408.2.a.bc	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$-$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots$
9408.2.a.bd	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$-$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots$
9408.2.a.be	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$+$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}+6q^{13}-2q^{15}+\cdots$
9408.2.a.bf	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$-$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots$
9408.2.a.bg	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$+$	$+$	$+$	$q-q^{3}+2q^{5}+q^{9}+2q^{11}-q^{13}+\cdots$
9408.2.a.bh	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$+$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots$
9408.2.a.bi	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$-$	$+$	$+$	$q-q^{3}+2q^{5}+q^{9}+2q^{11}+3q^{13}+\cdots$
9408.2.a.bj	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$+$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
9408.2.a.bk	$1$	$75.123$	$\Q$	None	$0$	$-1$	$2$	$0$	$+$	$+$	$-$	$q-q^{3}+2q^{5}+q^{9}+6q^{11}-3q^{13}+\cdots$
9408.2.a.bl	$1$	$75.123$	$\Q$	None	$0$	$-1$	$3$	$0$	$-$	$+$	$-$	$q-q^{3}+3q^{5}+q^{9}-q^{11}-4q^{13}+\cdots$
9408.2.a.bm	$1$	$75.123$	$\Q$	None	$0$	$-1$	$3$	$0$	$-$	$+$	$-$	$q-q^{3}+3q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots$
9408.2.a.bn	$1$	$75.123$	$\Q$	None	$0$	$-1$	$4$	$0$	$+$	$+$	$-$	$q-q^{3}+4q^{5}+q^{9}-2q^{11}-6q^{13}+\cdots$
9408.2.a.bo	$1$	$75.123$	$\Q$	None	$0$	$-1$	$4$	$0$	$+$	$+$	$-$	$q-q^{3}+4q^{5}+q^{9}+4q^{11}+4q^{13}+\cdots$
9408.2.a.bp	$1$	$75.123$	$\Q$	None	$0$	$-1$	$4$	$0$	$-$	$+$	$+$	$q-q^{3}+4q^{5}+q^{9}+6q^{11}-5q^{13}+\cdots$
9408.2.a.bq	$1$	$75.123$	$\Q$	None	$0$	$1$	$-4$	$0$	$+$	$-$	$-$	$q+q^{3}-4q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots$
9408.2.a.br	$1$	$75.123$	$\Q$	None	$0$	$1$	$-4$	$0$	$+$	$-$	$-$	$q+q^{3}-4q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots$
9408.2.a.bs	$1$	$75.123$	$\Q$	None	$0$	$1$	$-4$	$0$	$-$	$-$	$-$	$q+q^{3}-4q^{5}+q^{9}+6q^{11}+5q^{13}+\cdots$
9408.2.a.bt	$1$	$75.123$	$\Q$	None	$0$	$1$	$-3$	$0$	$-$	$-$	$+$	$q+q^{3}-3q^{5}+q^{9}-q^{11}+4q^{13}+\cdots$
9408.2.a.bu	$1$	$75.123$	$\Q$	None	$0$	$1$	$-3$	$0$	$-$	$-$	$+$	$q+q^{3}-3q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots$
9408.2.a.bv	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$+$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
9408.2.a.bw	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots$
9408.2.a.bx	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots$
9408.2.a.by	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$+$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots$
9408.2.a.bz	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$+$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}+2q^{11}+q^{13}+\cdots$
9408.2.a.ca	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots$
9408.2.a.cb	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots$
9408.2.a.cc	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$-$	$-$	$-$	$q+q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots$
9408.2.a.cd	$1$	$75.123$	$\Q$	None	$0$	$1$	$-2$	$0$	$+$	$-$	$+$	$q+q^{3}-2q^{5}+q^{9}+6q^{11}+3q^{13}+\cdots$
9408.2.a.ce	$1$	$75.123$	$\Q$	None	$0$	$1$	$-1$	$0$	$+$	$-$	$+$	$q+q^{3}-q^{5}+q^{9}-5q^{11}-q^{15}-4q^{17}+\cdots$
9408.2.a.cf	$1$	$75.123$	$\Q$	None	$0$	$1$	$-1$	$0$	$+$	$-$	$-$	$q+q^{3}-q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots$
9408.2.a.cg	$1$	$75.123$	$\Q$	None	$0$	$1$	$-1$	$0$	$-$	$-$	$+$	$q+q^{3}-q^{5}+q^{9}-q^{11}-q^{15}-8q^{17}+\cdots$
9408.2.a.ch	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}-2q^{11}-2q^{13}-4q^{17}+\cdots$
9408.2.a.ci	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}-2q^{11}+q^{13}+2q^{17}+\cdots$
9408.2.a.cj	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{9}-2q^{11}+5q^{13}+2q^{17}+\cdots$
9408.2.a.ck	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{9}-4q^{13}+4q^{17}-4q^{19}+\cdots$
9408.2.a.cl	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}+4q^{13}-4q^{17}-4q^{19}+\cdots$
9408.2.a.cm	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$-$	$-$	$+$	$q+q^{3}+q^{9}+2q^{11}-5q^{13}-2q^{17}+\cdots$
9408.2.a.cn	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$+$	$q+q^{3}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots$
9408.2.a.co	$1$	$75.123$	$\Q$	None	$0$	$1$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+q^{9}+6q^{11}+2q^{13}-4q^{19}+\cdots$
9408.2.a.cp	$1$	$75.123$	$\Q$	None	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{9}+q^{11}+q^{15}+8q^{17}+\cdots$
9408.2.a.cq	$1$	$75.123$	$\Q$	None	$0$	$1$	$1$	$0$	$-$	$-$	$+$	$q+q^{3}+q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots$
9408.2.a.cr	$1$	$75.123$	$\Q$	None	$0$	$1$	$1$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{5}+q^{9}+5q^{11}+q^{15}+4q^{17}+\cdots$
9408.2.a.cs	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$-$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}-6q^{11}-3q^{13}+\cdots$
9408.2.a.ct	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$+$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots$
9408.2.a.cu	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$+$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots$
9408.2.a.cv	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$-$	$-$	$+$	$q+q^{3}+2q^{5}+q^{9}-2q^{11}-q^{13}+\cdots$
9408.2.a.cw	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$+$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots$
9408.2.a.cx	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$+$	$-$	$+$	$q+q^{3}+2q^{5}+q^{9}-2q^{11}+3q^{13}+\cdots$
9408.2.a.cy	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$+$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots$
9408.2.a.cz	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$-$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots$
9408.2.a.da	$1$	$75.123$	$\Q$	None	$0$	$1$	$2$	$0$	$-$	$-$	$-$	$q+q^{3}+2q^{5}+q^{9}+6q^{13}+2q^{15}+\cdots$
9408.2.a.db	$1$	$75.123$	$\Q$	None	$0$	$1$	$3$	$0$	$+$	$-$	$-$	$q+q^{3}+3q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots$
9408.2.a.dc	$1$	$75.123$	$\Q$	None	$0$	$1$	$3$	$0$	$-$	$-$	$-$	$q+q^{3}+3q^{5}+q^{9}+q^{11}-4q^{13}+\cdots$
9408.2.a.dd	$1$	$75.123$	$\Q$	None	$0$	$1$	$4$	$0$	$-$	$-$	$+$	$q+q^{3}+4q^{5}+q^{9}-6q^{11}-5q^{13}+\cdots$
9408.2.a.de	$1$	$75.123$	$\Q$	None	$0$	$1$	$4$	$0$	$-$	$-$	$-$	$q+q^{3}+4q^{5}+q^{9}-4q^{11}+4q^{13}+\cdots$
9408.2.a.df	$1$	$75.123$	$\Q$	None	$0$	$1$	$4$	$0$	$-$	$-$	$-$	$q+q^{3}+4q^{5}+q^{9}+2q^{11}-6q^{13}+\cdots$
9408.2.a.dg	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$-4$	$0$	$+$	$+$	$+$	$q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots$
9408.2.a.dh	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$-4$	$0$	$-$	$+$	$+$	$q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots$
9408.2.a.di	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$-4$	$0$	$+$	$+$	$+$	$q-q^{3}+(-2+\beta )q^{5}+q^{9}+2q^{11}+\cdots$
9408.2.a.dj	$2$	$75.123$	$\Q(\sqrt{57}) $	None	$0$	$-2$	$-1$	$0$	$+$	$+$	$-$	$q-q^{3}-\beta q^{5}+q^{9}+\beta q^{11}+(3-\beta )q^{13}+\cdots$
9408.2.a.dk	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}-\beta q^{15}+\cdots$
9408.2.a.dl	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$0$	$-$	$+$	$+$	$q-q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}+\beta q^{13}+\cdots$
9408.2.a.dm	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+q^{9}+\beta q^{11}-\beta q^{13}+\beta q^{17}+\cdots$
9408.2.a.dn	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$0$	$0$	$-$	$+$	$+$	$q-q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}-3\beta q^{13}+\cdots$
9408.2.a.do	$2$	$75.123$	$\Q(\sqrt{3}) $	None	$0$	$-2$	$0$	$0$	$-$	$+$	$-$	$q-q^{3}+\beta q^{5}+q^{9}+(2-\beta )q^{11}+2q^{13}+\cdots$
9408.2.a.dp	$2$	$75.123$	$\Q(\sqrt{57}) $	None	$0$	$-2$	$1$	$0$	$-$	$+$	$+$	$q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+(-3+\beta )q^{13}+\cdots$
9408.2.a.dq	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$4$	$0$	$-$	$+$	$+$	$q-q^{3}+(2+\beta )q^{5}+q^{9}-2q^{11}+(4+\cdots)q^{13}+\cdots$
9408.2.a.dr	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$4$	$0$	$+$	$+$	$+$	$q-q^{3}+(2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots$
9408.2.a.ds	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$-2$	$4$	$0$	$-$	$+$	$+$	$q-q^{3}+(2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots$
9408.2.a.dt	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$-4$	$0$	$-$	$-$	$+$	$q+q^{3}+(-2+\beta )q^{5}+q^{9}-2q^{11}+\cdots$
9408.2.a.du	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$-4$	$0$	$-$	$-$	$+$	$q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots$
9408.2.a.dv	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$-4$	$0$	$+$	$-$	$+$	$q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots$
9408.2.a.dw	$2$	$75.123$	$\Q(\sqrt{57}) $	None	$0$	$2$	$-1$	$0$	$-$	$-$	$-$	$q+q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(3-\beta )q^{13}+\cdots$
9408.2.a.dx	$2$	$75.123$	$\Q(\sqrt{3}) $	None	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$q+q^{3}+\beta q^{5}+q^{9}+(-2+\beta )q^{11}+\cdots$
9408.2.a.dy	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$q+q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}-3\beta q^{13}+\cdots$
9408.2.a.dz	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$q+q^{3}+q^{9}+\beta q^{11}+\beta q^{13}-\beta q^{17}+\cdots$
9408.2.a.ea	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$0$	$-$	$-$	$+$	$q+q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+\beta q^{13}+\cdots$
9408.2.a.eb	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$0$	$0$	$-$	$-$	$-$	$q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+\beta q^{15}+\cdots$
9408.2.a.ec	$2$	$75.123$	$\Q(\sqrt{57}) $	None	$0$	$2$	$1$	$0$	$+$	$-$	$+$	$q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+(-3+\beta )q^{13}+\cdots$
9408.2.a.ed	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$4$	$0$	$-$	$-$	$+$	$q+q^{3}+(2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots$
9408.2.a.ee	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$4$	$0$	$+$	$-$	$+$	$q+q^{3}+(2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots$
9408.2.a.ef	$2$	$75.123$	$\Q(\sqrt{2}) $	None	$0$	$2$	$4$	$0$	$+$	$-$	$+$	$q+q^{3}+(2+\beta )q^{5}+q^{9}+2q^{11}+(4+\cdots)q^{13}+\cdots$
9408.2.a.eg	$3$	$75.123$	3.3.621.1	None	$0$	$-3$	$0$	$0$	$+$	$+$	$-$	$q-q^{3}+\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots$
9408.2.a.eh	$3$	$75.123$	3.3.621.1	None	$0$	$-3$	$0$	$0$	$+$	$+$	$+$	$q-q^{3}-\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots$
9408.2.a.ei	$3$	$75.123$	3.3.621.1	None	$0$	$3$	$0$	$0$	$+$	$-$	$-$	$q+q^{3}+\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots$
9408.2.a.ej	$3$	$75.123$	3.3.621.1	None	$0$	$3$	$0$	$0$	$+$	$-$	$+$	$q+q^{3}-\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots$
9408.2.a.ek	$4$	$75.123$	4.4.2624.1	None	$0$	$-4$	$-4$	$0$	$+$	$+$	$+$	$q-q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots$
9408.2.a.el	$4$	$75.123$	4.4.2624.1	None	$0$	$-4$	$4$	$0$	$+$	$+$	$+$	$q-q^{3}+(1+\beta _{3})q^{5}+q^{9}+(1+\beta _{2})q^{11}+\cdots$
9408.2.a.em	$4$	$75.123$	4.4.2624.1	None	$0$	$4$	$-4$	$0$	$+$	$-$	$+$	$q+q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots$
9408.2.a.en	$4$	$75.123$	4.4.2624.1	None	$0$	$4$	$4$	$0$	$+$	$-$	$+$	$q+q^{3}+(1+\beta _{3})q^{5}+q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(9408))$ into lower level spaces

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9408 = 2^{6} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9408.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 118 \)
Sturm bound:			\(3584\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\), \(19\), \(31\)

\(2\)	\(3\)	\(7\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(21\)
\(+\)	\(+\)	\(-\)	\(-\)	\(21\)
\(+\)	\(-\)	\(+\)	\(-\)	\(23\)
\(+\)	\(-\)	\(-\)	\(+\)	\(18\)
\(-\)	\(+\)	\(+\)	\(-\)	\(19\)
\(-\)	\(+\)	\(-\)	\(+\)	\(21\)
\(-\)	\(-\)	\(+\)	\(+\)	\(17\)
\(-\)	\(-\)	\(-\)	\(-\)	\(24\)
Plus space			\(+\)	\(77\)
Minus space			\(-\)	\(87\)

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Fields

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9408))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9408))\) 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	9408.2.a

Level	$9408$
Weight	$2$
Character orbit	9408.a
Rep. character	$\chi_{9408}(1,\cdot)$
Character field	$\Q$
Dimension	$164$
Newform subspaces	$118$
Sturm bound	$3584$
Trace bound	$19$

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	7	$q$-expansion
9408.2.a.a	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-4\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}-4q^{5}+q^{9}-6q^{11}+5q^{13}+\cdots\)
9408.2.a.b	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-4\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}-4q^{5}+q^{9}-4q^{11}-4q^{13}+\cdots\)
9408.2.a.c	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-4\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}-4q^{5}+q^{9}-2q^{11}-2q^{13}+\cdots\)
9408.2.a.d	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-3\)	\(0\)	$+$	$+$	$+$	\(q-q^{3}-3q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
9408.2.a.e	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-3\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}-3q^{5}+q^{9}+q^{11}+4q^{13}+\cdots\)
9408.2.a.f	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}-2q^{5}+q^{9}-6q^{11}+3q^{13}+\cdots\)
9408.2.a.g	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}-2q^{5}+q^{9}-4q^{11}-6q^{13}+\cdots\)
9408.2.a.h	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9408.2.a.i	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}-2q^{5}+q^{9}-2q^{11}-3q^{13}+\cdots\)
9408.2.a.j	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}-2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots\)
9408.2.a.k	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}-2q^{5}+q^{9}-2q^{11}+q^{13}+\cdots\)
9408.2.a.l	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}-2q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots\)
9408.2.a.m	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9408.2.a.n	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-2\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}+6q^{13}+\cdots\)
9408.2.a.o	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}-q^{5}+q^{9}+q^{11}+q^{15}-8q^{17}+\cdots\)
9408.2.a.p	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}-q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots\)
9408.2.a.q	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(-1\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}-q^{5}+q^{9}+5q^{11}+q^{15}-4q^{17}+\cdots\)
9408.2.a.r	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}+q^{9}-6q^{11}+2q^{13}+4q^{19}+\cdots\)
9408.2.a.s	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}+q^{9}-2q^{11}-5q^{13}-2q^{17}+\cdots\)
9408.2.a.t	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	$+$	$+$	$+$	\(q-q^{3}+q^{9}-2q^{11}-q^{13}-2q^{17}+\cdots\)
9408.2.a.u	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}+q^{9}-4q^{13}+4q^{17}+4q^{19}+\cdots\)
9408.2.a.v	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}+q^{9}+4q^{13}-4q^{17}+4q^{19}+\cdots\)
9408.2.a.w	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}+q^{9}+2q^{11}-2q^{13}-4q^{17}+\cdots\)
9408.2.a.x	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}+q^{9}+2q^{11}+q^{13}+2q^{17}+\cdots\)
9408.2.a.y	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(0\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}+q^{9}+2q^{11}+5q^{13}+2q^{17}+\cdots\)
9408.2.a.z	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}+q^{5}+q^{9}-5q^{11}-q^{15}+4q^{17}+\cdots\)
9408.2.a.ba	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(0\)	$+$	$+$	$+$	\(q-q^{3}+q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
9408.2.a.bb	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(1\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}+q^{5}+q^{9}-q^{11}-q^{15}+8q^{17}+\cdots\)
9408.2.a.bc	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}+2q^{5}+q^{9}-2q^{13}-2q^{15}+\cdots\)
9408.2.a.bd	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}+2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots\)
9408.2.a.be	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}+2q^{5}+q^{9}+6q^{13}-2q^{15}+\cdots\)
9408.2.a.bf	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
9408.2.a.bg	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	$+$	$+$	$+$	\(q-q^{3}+2q^{5}+q^{9}+2q^{11}-q^{13}+\cdots\)
9408.2.a.bh	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}+2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots\)
9408.2.a.bi	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}+2q^{5}+q^{9}+2q^{11}+3q^{13}+\cdots\)
9408.2.a.bj	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}+2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9408.2.a.bk	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(2\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}+2q^{5}+q^{9}+6q^{11}-3q^{13}+\cdots\)
9408.2.a.bl	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(3\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}+3q^{5}+q^{9}-q^{11}-4q^{13}+\cdots\)
9408.2.a.bm	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(3\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}+3q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots\)
9408.2.a.bn	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(4\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}+4q^{5}+q^{9}-2q^{11}-6q^{13}+\cdots\)
9408.2.a.bo	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(4\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}+4q^{5}+q^{9}+4q^{11}+4q^{13}+\cdots\)
9408.2.a.bp	$1$	$75.123$	\(\Q\)	None	\(0\)	\(-1\)	\(4\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}+4q^{5}+q^{9}+6q^{11}-5q^{13}+\cdots\)
9408.2.a.bq	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-4\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}-4q^{5}+q^{9}+2q^{11}-2q^{13}+\cdots\)
9408.2.a.br	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-4\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}-4q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots\)
9408.2.a.bs	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-4\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}-4q^{5}+q^{9}+6q^{11}+5q^{13}+\cdots\)
9408.2.a.bt	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-3\)	\(0\)	$-$	$-$	$+$	\(q+q^{3}-3q^{5}+q^{9}-q^{11}+4q^{13}+\cdots\)
9408.2.a.bu	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-3\)	\(0\)	$-$	$-$	$+$	\(q+q^{3}-3q^{5}+q^{9}+3q^{11}+4q^{13}+\cdots\)
9408.2.a.bv	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}-2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9408.2.a.bw	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}-2q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)
9408.2.a.bx	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots\)
9408.2.a.by	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}-2q^{15}+\cdots\)
9408.2.a.bz	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}+q^{13}+\cdots\)
9408.2.a.ca	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
9408.2.a.cb	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}-2q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
9408.2.a.cc	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
9408.2.a.cd	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-2\)	\(0\)	$+$	$-$	$+$	\(q+q^{3}-2q^{5}+q^{9}+6q^{11}+3q^{13}+\cdots\)
9408.2.a.ce	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(0\)	$+$	$-$	$+$	\(q+q^{3}-q^{5}+q^{9}-5q^{11}-q^{15}-4q^{17}+\cdots\)
9408.2.a.cf	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}-q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
9408.2.a.cg	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(-1\)	\(0\)	$-$	$-$	$+$	\(q+q^{3}-q^{5}+q^{9}-q^{11}-q^{15}-8q^{17}+\cdots\)
9408.2.a.ch	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}+q^{9}-2q^{11}-2q^{13}-4q^{17}+\cdots\)
9408.2.a.ci	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}+q^{9}-2q^{11}+q^{13}+2q^{17}+\cdots\)
9408.2.a.cj	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+q^{9}-2q^{11}+5q^{13}+2q^{17}+\cdots\)
9408.2.a.ck	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+q^{9}-4q^{13}+4q^{17}-4q^{19}+\cdots\)
9408.2.a.cl	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}+q^{9}+4q^{13}-4q^{17}-4q^{19}+\cdots\)
9408.2.a.cm	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	$-$	$-$	$+$	\(q+q^{3}+q^{9}+2q^{11}-5q^{13}-2q^{17}+\cdots\)
9408.2.a.cn	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	$+$	$-$	$+$	\(q+q^{3}+q^{9}+2q^{11}-q^{13}-2q^{17}+\cdots\)
9408.2.a.co	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(0\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}+q^{9}+6q^{11}+2q^{13}-4q^{19}+\cdots\)
9408.2.a.cp	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+q^{5}+q^{9}+q^{11}+q^{15}+8q^{17}+\cdots\)
9408.2.a.cq	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(0\)	$-$	$-$	$+$	\(q+q^{3}+q^{5}+q^{9}+3q^{11}-4q^{13}+\cdots\)
9408.2.a.cr	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(1\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+q^{5}+q^{9}+5q^{11}+q^{15}+4q^{17}+\cdots\)
9408.2.a.cs	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+2q^{5}+q^{9}-6q^{11}-3q^{13}+\cdots\)
9408.2.a.ct	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
9408.2.a.cu	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}+2q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\)
9408.2.a.cv	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	$-$	$-$	$+$	\(q+q^{3}+2q^{5}+q^{9}-2q^{11}-q^{13}+\cdots\)
9408.2.a.cw	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}+2q^{5}+q^{9}-2q^{11}+2q^{15}+\cdots\)
9408.2.a.cx	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	$+$	$-$	$+$	\(q+q^{3}+2q^{5}+q^{9}-2q^{11}+3q^{13}+\cdots\)
9408.2.a.cy	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}+2q^{5}+q^{9}-2q^{13}+2q^{15}+\cdots\)
9408.2.a.cz	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+2q^{5}+q^{9}+2q^{13}+2q^{15}+\cdots\)
9408.2.a.da	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(2\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+2q^{5}+q^{9}+6q^{13}+2q^{15}+\cdots\)
9408.2.a.db	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(3\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}+3q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
9408.2.a.dc	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(3\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+3q^{5}+q^{9}+q^{11}-4q^{13}+\cdots\)
9408.2.a.dd	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(4\)	\(0\)	$-$	$-$	$+$	\(q+q^{3}+4q^{5}+q^{9}-6q^{11}-5q^{13}+\cdots\)
9408.2.a.de	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(4\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+4q^{5}+q^{9}-4q^{11}+4q^{13}+\cdots\)
9408.2.a.df	$1$	$75.123$	\(\Q\)	None	\(0\)	\(1\)	\(4\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+4q^{5}+q^{9}+2q^{11}-6q^{13}+\cdots\)
9408.2.a.dg	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(-4\)	\(0\)	$+$	$+$	$+$	\(q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
9408.2.a.dh	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(-4\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}+(-2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots\)
9408.2.a.di	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(-4\)	\(0\)	$+$	$+$	$+$	\(q-q^{3}+(-2+\beta )q^{5}+q^{9}+2q^{11}+\cdots\)
9408.2.a.dj	$2$	$75.123$	\(\Q(\sqrt{57}) \)	None	\(0\)	\(-2\)	\(-1\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}-\beta q^{5}+q^{9}+\beta q^{11}+(3-\beta )q^{13}+\cdots\)
9408.2.a.dk	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}-\beta q^{15}+\cdots\)
9408.2.a.dl	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}+\beta q^{13}+\cdots\)
9408.2.a.dm	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}+q^{9}+\beta q^{11}-\beta q^{13}+\beta q^{17}+\cdots\)
9408.2.a.dn	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}-3\beta q^{13}+\cdots\)
9408.2.a.do	$2$	$75.123$	\(\Q(\sqrt{3}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)	$-$	$+$	$-$	\(q-q^{3}+\beta q^{5}+q^{9}+(2-\beta )q^{11}+2q^{13}+\cdots\)
9408.2.a.dp	$2$	$75.123$	\(\Q(\sqrt{57}) \)	None	\(0\)	\(-2\)	\(1\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+(-3+\beta )q^{13}+\cdots\)
9408.2.a.dq	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(4\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}+(2+\beta )q^{5}+q^{9}-2q^{11}+(4+\cdots)q^{13}+\cdots\)
9408.2.a.dr	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(4\)	\(0\)	$+$	$+$	$+$	\(q-q^{3}+(2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots\)
9408.2.a.ds	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(-2\)	\(4\)	\(0\)	$-$	$+$	$+$	\(q-q^{3}+(2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
9408.2.a.dt	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(-4\)	\(0\)	$-$	$-$	$+$	\(q+q^{3}+(-2+\beta )q^{5}+q^{9}-2q^{11}+\cdots\)
9408.2.a.du	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(-4\)	\(0\)	$-$	$-$	$+$	\(q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots\)
9408.2.a.dv	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(-4\)	\(0\)	$+$	$-$	$+$	\(q+q^{3}+(-2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
9408.2.a.dw	$2$	$75.123$	\(\Q(\sqrt{57}) \)	None	\(0\)	\(2\)	\(-1\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(3-\beta )q^{13}+\cdots\)
9408.2.a.dx	$2$	$75.123$	\(\Q(\sqrt{3}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+\beta q^{5}+q^{9}+(-2+\beta )q^{11}+\cdots\)
9408.2.a.dy	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	$-$	$-$	$+$	\(q+q^{3}+\beta q^{5}+q^{9}+2\beta q^{11}-3\beta q^{13}+\cdots\)
9408.2.a.dz	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+q^{9}+\beta q^{11}+\beta q^{13}-\beta q^{17}+\cdots\)
9408.2.a.ea	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	$-$	$-$	$+$	\(q+q^{3}+\beta q^{5}+q^{9}-2\beta q^{11}+\beta q^{13}+\cdots\)
9408.2.a.eb	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)	$-$	$-$	$-$	\(q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+\beta q^{15}+\cdots\)
9408.2.a.ec	$2$	$75.123$	\(\Q(\sqrt{57}) \)	None	\(0\)	\(2\)	\(1\)	\(0\)	$+$	$-$	$+$	\(q+q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+(-3+\beta )q^{13}+\cdots\)
9408.2.a.ed	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(4\)	\(0\)	$-$	$-$	$+$	\(q+q^{3}+(2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
9408.2.a.ee	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(4\)	\(0\)	$+$	$-$	$+$	\(q+q^{3}+(2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots\)
9408.2.a.ef	$2$	$75.123$	\(\Q(\sqrt{2}) \)	None	\(0\)	\(2\)	\(4\)	\(0\)	$+$	$-$	$+$	\(q+q^{3}+(2+\beta )q^{5}+q^{9}+2q^{11}+(4+\cdots)q^{13}+\cdots\)
9408.2.a.eg	$3$	$75.123$	3.3.621.1	None	\(0\)	\(-3\)	\(0\)	\(0\)	$+$	$+$	$-$	\(q-q^{3}+\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9408.2.a.eh	$3$	$75.123$	3.3.621.1	None	\(0\)	\(-3\)	\(0\)	\(0\)	$+$	$+$	$+$	\(q-q^{3}-\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
9408.2.a.ei	$3$	$75.123$	3.3.621.1	None	\(0\)	\(3\)	\(0\)	\(0\)	$+$	$-$	$-$	\(q+q^{3}+\beta _{2}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{11}+\cdots\)
9408.2.a.ej	$3$	$75.123$	3.3.621.1	None	\(0\)	\(3\)	\(0\)	\(0\)	$+$	$-$	$+$	\(q+q^{3}-\beta _{2}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
9408.2.a.ek	$4$	$75.123$	4.4.2624.1	None	\(0\)	\(-4\)	\(-4\)	\(0\)	$+$	$+$	$+$	\(q-q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(-1+\beta _{2}+\cdots)q^{11}+\cdots\)
9408.2.a.el	$4$	$75.123$	4.4.2624.1	None	\(0\)	\(-4\)	\(4\)	\(0\)	$+$	$+$	$+$	\(q-q^{3}+(1+\beta _{3})q^{5}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
9408.2.a.em	$4$	$75.123$	4.4.2624.1	None	\(0\)	\(4\)	\(-4\)	\(0\)	$+$	$-$	$+$	\(q+q^{3}+(-1+\beta _{3})q^{5}+q^{9}+(1-\beta _{2}+\cdots)q^{11}+\cdots\)
9408.2.a.en	$4$	$75.123$	4.4.2624.1	None	\(0\)	\(4\)	\(4\)	\(0\)	$+$	$-$	$+$	\(q+q^{3}+(1+\beta _{3})q^{5}+q^{9}+(-1-\beta _{2}+\cdots)q^{11}+\cdots\)