LMFDB - Space of modular forms of level 7605, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 7605 = 3^{2} \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7605.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 77 $
Sturm bound:			$2184$
Trace bound:			$11$
Distinguishing $T_p$:			$2$, $7$, $11$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(7605))$.

	Total	New	Old
Modular forms	1148	259	889
Cusp forms	1037	259	778
Eisenstein series	111	0	111

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

$3$	$5$	$13$	Fricke	Dim.
$+$	$+$	$+$	$+$	$26$
$+$	$+$	$-$	$-$	$26$
$+$	$-$	$+$	$-$	$26$
$+$	$-$	$-$	$+$	$26$
$-$	$+$	$+$	$-$	$42$
$-$	$+$	$-$	$+$	$36$
$-$	$-$	$+$	$+$	$35$
$-$	$-$	$-$	$-$	$42$
Plus space			$+$	$123$
Minus space			$-$	$136$

Trace form

$ 259q + q^{2} + 261q^{4} - q^{5} + 4q^{7} + 9q^{8} + O(q^{10}) $

$ 259q + q^{2} + 261q^{4} - q^{5} + 4q^{7} + 9q^{8} - 3q^{10} - 20q^{14} + 261q^{16} - 6q^{17} + 4q^{19} - 7q^{20} + 16q^{22} + 259q^{25} + 12q^{28} + 10q^{29} - 12q^{31} - 11q^{32} + 2q^{34} + 4q^{35} + 10q^{37} - 3q^{40} - 18q^{41} + 12q^{43} - 28q^{44} + 32q^{46} + 4q^{47} + 275q^{49} + q^{50} + 10q^{53} + 4q^{55} - 40q^{56} + 6q^{58} - 4q^{59} - 22q^{61} + 241q^{64} + 24q^{67} - 6q^{68} - 8q^{70} + 16q^{71} + 14q^{73} + 22q^{74} + 48q^{76} + 20q^{77} + 12q^{79} - 15q^{80} - 42q^{82} - 32q^{83} - 10q^{85} + 76q^{86} + 52q^{88} + 2q^{89} + 20q^{92} - 60q^{94} + 12q^{95} + 18q^{97} - 31q^{98} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(7605))$ into newform subspaces

Label	Dim.	$A$	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	$A$	Field	CM	$a_2$	$a_3$	$a_5$	$a_7$	3	5	13	$q$-expansion
7605.2.a.a	$1$	$60.726$	$\Q$	None	$-2$	$0$	$1$	$5$	$-$	$-$	$+$	$q-2q^{2}+2q^{4}+q^{5}+5q^{7}-2q^{10}+\cdots$
7605.2.a.b	$1$	$60.726$	$\Q$	None	$-1$	$0$	$-1$	$-4$	$+$	$+$	$-$	$q-q^{2}-q^{4}-q^{5}-4q^{7}+3q^{8}+q^{10}+\cdots$
7605.2.a.c	$1$	$60.726$	$\Q$	None	$-1$	$0$	$-1$	$-2$	$+$	$+$	$+$	$q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots$
7605.2.a.d	$1$	$60.726$	$\Q$	None	$-1$	$0$	$-1$	$2$	$-$	$+$	$-$	$q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots$
7605.2.a.e	$1$	$60.726$	$\Q$	None	$-1$	$0$	$-1$	$4$	$+$	$+$	$-$	$q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots$
7605.2.a.f	$1$	$60.726$	$\Q$	None	$-1$	$0$	$-1$	$4$	$-$	$+$	$+$	$q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots$
7605.2.a.g	$1$	$60.726$	$\Q$	None	$-1$	$0$	$1$	$0$	$-$	$-$	$+$	$q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}-4q^{11}+\cdots$
7605.2.a.h	$1$	$60.726$	$\Q$	None	$-1$	$0$	$1$	$0$	$-$	$-$	$+$	$q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}+4q^{11}+\cdots$
7605.2.a.i	$1$	$60.726$	$\Q$	None	$0$	$0$	$-1$	$-3$	$-$	$+$	$-$	$q-2q^{4}-q^{5}-3q^{7}-3q^{11}+4q^{16}+\cdots$
7605.2.a.j	$1$	$60.726$	$\Q$	None	$0$	$0$	$-1$	$1$	$+$	$+$	$+$	$q-2q^{4}-q^{5}+q^{7}+3q^{11}+4q^{16}+\cdots$
7605.2.a.k	$1$	$60.726$	$\Q$	None	$0$	$0$	$-1$	$1$	$-$	$+$	$+$	$q-2q^{4}-q^{5}+q^{7}+6q^{11}+4q^{16}+\cdots$
7605.2.a.l	$1$	$60.726$	$\Q$	None	$0$	$0$	$1$	$-1$	$-$	$-$	$+$	$q-2q^{4}+q^{5}-q^{7}-6q^{11}+4q^{16}+\cdots$
7605.2.a.m	$1$	$60.726$	$\Q$	None	$0$	$0$	$1$	$1$	$+$	$-$	$+$	$q-2q^{4}+q^{5}+q^{7}-3q^{11}+4q^{16}+\cdots$
7605.2.a.n	$1$	$60.726$	$\Q$	None	$0$	$0$	$1$	$3$	$-$	$-$	$-$	$q-2q^{4}+q^{5}+3q^{7}+3q^{11}+4q^{16}+\cdots$
7605.2.a.o	$1$	$60.726$	$\Q$	None	$1$	$0$	$1$	$-4$	$+$	$-$	$-$	$q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots$
7605.2.a.p	$1$	$60.726$	$\Q$	None	$1$	$0$	$1$	$-2$	$-$	$-$	$-$	$q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots$
7605.2.a.q	$1$	$60.726$	$\Q$	None	$1$	$0$	$1$	$-2$	$+$	$-$	$+$	$q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots$
7605.2.a.r	$1$	$60.726$	$\Q$	None	$1$	$0$	$1$	$4$	$+$	$-$	$-$	$q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots$
7605.2.a.s	$1$	$60.726$	$\Q$	None	$2$	$0$	$-1$	$-5$	$-$	$+$	$+$	$q+2q^{2}+2q^{4}-q^{5}-5q^{7}-2q^{10}+\cdots$
7605.2.a.t	$1$	$60.726$	$\Q$	None	$2$	$0$	$-1$	$1$	$-$	$+$	$+$	$q+2q^{2}+2q^{4}-q^{5}+q^{7}-2q^{10}+\cdots$
7605.2.a.u	$1$	$60.726$	$\Q$	None	$2$	$0$	$1$	$-3$	$-$	$-$	$+$	$q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots$
7605.2.a.v	$1$	$60.726$	$\Q$	None	$2$	$0$	$1$	$3$	$-$	$-$	$+$	$q+2q^{2}+2q^{4}+q^{5}+3q^{7}+2q^{10}+\cdots$
7605.2.a.w	$2$	$60.726$	$\Q(\sqrt{13}) $	None	$-4$	$0$	$2$	$0$	$+$	$-$	$-$	$q-2q^{2}+2q^{4}+q^{5}-\beta q^{7}-2q^{10}+\cdots$
7605.2.a.x	$2$	$60.726$	$\Q(\sqrt{2}) $	None	$-2$	$0$	$2$	$-4$	$-$	$-$	$+$	$q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots$
7605.2.a.y	$2$	$60.726$	$\Q(\sqrt{3}) $	None	$-2$	$0$	$-2$	$-2$	$-$	$+$	$-$	$q+(-1+\beta )q^{2}+(2-2\beta )q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots$
7605.2.a.z	$2$	$60.726$	$\Q(\sqrt{3}) $	None	$-2$	$0$	$2$	$0$	$-$	$-$	$+$	$q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+q^{5}+\beta q^{7}+\cdots$
7605.2.a.ba	$2$	$60.726$	$\Q(\sqrt{5}) $	None	$-1$	$0$	$-2$	$4$	$-$	$+$	$+$	$q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(3-2\beta )q^{7}+\cdots$
7605.2.a.bb	$2$	$60.726$	$\Q(\sqrt{13}) $	None	$-1$	$0$	$-2$	$2$	$-$	$+$	$+$	$q-\beta q^{2}+(1+\beta )q^{4}-q^{5}+q^{7}-3q^{8}+\cdots$
7605.2.a.bc	$2$	$60.726$	$\Q(\sqrt{17}) $	None	$-1$	$0$	$-2$	$-3$	$-$	$+$	$-$	$q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(-1-\beta )q^{7}+\cdots$
7605.2.a.bd	$2$	$60.726$	$\Q(\sqrt{17}) $	None	$-1$	$0$	$-2$	$5$	$+$	$+$	$+$	$q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(3-\beta )q^{7}+\cdots$
7605.2.a.be	$2$	$60.726$	$\Q(\sqrt{3}) $	None	$0$	$0$	$-2$	$-4$	$-$	$+$	$+$	$q+\beta q^{2}+q^{4}-q^{5}-2q^{7}-\beta q^{8}-\beta q^{10}+\cdots$
7605.2.a.bf	$2$	$60.726$	$\Q(\sqrt{5}) $	None	$1$	$0$	$2$	$-4$	$-$	$-$	$+$	$q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-3+2\beta )q^{7}+\cdots$
7605.2.a.bg	$2$	$60.726$	$\Q(\sqrt{13}) $	None	$1$	$0$	$2$	$-2$	$-$	$-$	$+$	$q+\beta q^{2}+(1+\beta )q^{4}+q^{5}-q^{7}+3q^{8}+\cdots$
7605.2.a.bh	$2$	$60.726$	$\Q(\sqrt{17}) $	None	$1$	$0$	$2$	$3$	$-$	$-$	$-$	$q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(1+\beta )q^{7}+\cdots$
7605.2.a.bi	$2$	$60.726$	$\Q(\sqrt{17}) $	None	$1$	$0$	$2$	$5$	$+$	$-$	$+$	$q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(3-\beta )q^{7}+\cdots$
7605.2.a.bj	$2$	$60.726$	$\Q(\sqrt{3}) $	None	$2$	$0$	$-2$	$0$	$-$	$+$	$+$	$q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}+\beta q^{7}+\cdots$
7605.2.a.bk	$2$	$60.726$	$\Q(\sqrt{3}) $	None	$2$	$0$	$2$	$2$	$-$	$-$	$-$	$q+(1+\beta )q^{2}+(2+2\beta )q^{4}+q^{5}+(1-2\beta )q^{7}+\cdots$
7605.2.a.bl	$2$	$60.726$	$\Q(\sqrt{13}) $	None	$4$	$0$	$-2$	$0$	$+$	$+$	$-$	$q+2q^{2}+2q^{4}-q^{5}+\beta q^{7}-2q^{10}+\cdots$
7605.2.a.bm	$3$	$60.726$	$\Q(\zeta_{14})^+$	None	$-3$	$0$	$3$	$0$	$-$	$-$	$+$	$q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots$
7605.2.a.bn	$3$	$60.726$	$\Q(\zeta_{14})^+$	None	$-2$	$0$	$-3$	$-4$	$-$	$+$	$-$	$q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots$
7605.2.a.bo	$3$	$60.726$	$\Q(\zeta_{14})^+$	None	$-1$	$0$	$-3$	$-4$	$-$	$+$	$+$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
7605.2.a.bp	$3$	$60.726$	$\Q(\zeta_{14})^+$	None	$-1$	$0$	$3$	$-12$	$-$	$-$	$+$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}-4q^{7}+(-1+\cdots)q^{8}+\cdots$
7605.2.a.bq	$3$	$60.726$	$\Q(\zeta_{14})^+$	None	$-1$	$0$	$3$	$-2$	$-$	$-$	$+$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$
7605.2.a.br	$3$	$60.726$	$\Q(\zeta_{14})^+$	None	$-1$	$0$	$3$	$5$	$-$	$-$	$+$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots$
7605.2.a.bs	$3$	$60.726$	3.3.564.1	None	$-1$	$0$	$3$	$2$	$-$	$-$	$-$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1+\beta _{2})q^{7}+\cdots$
7605.2.a.bt	$3$	$60.726$	3.3.148.1	None	$0$	$0$	$-3$	$5$	$-$	$+$	$+$	$q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots$
7605.2.a.bu	$3$	$60.726$	3.3.148.1	None	$0$	$0$	$3$	$-5$	$-$	$-$	$+$	$q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots$
7605.2.a.bv	$3$	$60.726$	3.3.756.1	None	$0$	$0$	$-3$	$3$	$-$	$+$	$+$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots$
7605.2.a.bw	$3$	$60.726$	3.3.756.1	None	$0$	$0$	$3$	$-3$	$-$	$-$	$+$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
7605.2.a.bx	$3$	$60.726$	3.3.316.1	None	$0$	$0$	$-3$	$-1$	$-$	$+$	$+$	$q-\beta _{1}q^{2}+(3+\beta _{2})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots$
7605.2.a.by	$3$	$60.726$	$\Q(\zeta_{14})^+$	None	$1$	$0$	$-3$	$-5$	$-$	$+$	$-$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots$
7605.2.a.bz	$3$	$60.726$	$\Q(\zeta_{14})^+$	None	$1$	$0$	$-3$	$2$	$-$	$+$	$-$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(1-\beta _{1})q^{7}+\cdots$
7605.2.a.ca	$3$	$60.726$	$\Q(\zeta_{14})^+$	None	$1$	$0$	$-3$	$12$	$-$	$+$	$-$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+4q^{7}+(1-2\beta _{1}+\cdots)q^{8}+\cdots$
7605.2.a.cb	$3$	$60.726$	$\Q(\zeta_{14})^+$	None	$1$	$0$	$3$	$4$	$-$	$-$	$-$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(1+\beta _{1})q^{7}+\cdots$
7605.2.a.cc	$3$	$60.726$	3.3.564.1	None	$1$	$0$	$-3$	$-2$	$-$	$+$	$-$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1-\beta _{2})q^{7}+\cdots$
7605.2.a.cd	$3$	$60.726$	$\Q(\zeta_{14})^+$	None	$2$	$0$	$3$	$4$	$-$	$-$	$+$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots$
7605.2.a.ce	$3$	$60.726$	$\Q(\zeta_{14})^+$	None	$3$	$0$	$-3$	$0$	$-$	$+$	$-$	$q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}-q^{5}+\cdots$
7605.2.a.cf	$4$	$60.726$	4.4.4752.1	None	$-2$	$0$	$4$	$10$	$-$	$-$	$-$	$q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+(3+\beta _{2}+\cdots)q^{7}+\cdots$
7605.2.a.cg	$4$	$60.726$	4.4.7488.1	None	$-2$	$0$	$-4$	$6$	$-$	$+$	$-$	$q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}-q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots$
7605.2.a.ch	$4$	$60.726$	4.4.13824.1	None	$0$	$0$	$-4$	$0$	$-$	$+$	$-$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
7605.2.a.ci	$4$	$60.726$	4.4.13824.1	None	$0$	$0$	$4$	$0$	$-$	$-$	$-$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots$
7605.2.a.cj	$4$	$60.726$	4.4.4752.1	None	$2$	$0$	$-4$	$-10$	$-$	$+$	$-$	$q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(-3+\cdots)q^{7}+\cdots$
7605.2.a.ck	$4$	$60.726$	4.4.7488.1	None	$2$	$0$	$4$	$-6$	$-$	$-$	$-$	$q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots$
7605.2.a.cl	$5$	$60.726$	5.5.3352656.1	None	$-2$	$0$	$-5$	$-1$	$+$	$+$	$+$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{4}q^{7}+\cdots$
7605.2.a.cm	$5$	$60.726$	5.5.3352656.1	None	$-2$	$0$	$-5$	$1$	$+$	$+$	$+$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{4}q^{7}+\cdots$
7605.2.a.cn	$5$	$60.726$	5.5.3352656.1	None	$2$	$0$	$5$	$-1$	$+$	$-$	$+$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{4}q^{7}+\cdots$
7605.2.a.co	$5$	$60.726$	5.5.3352656.1	None	$2$	$0$	$5$	$1$	$+$	$-$	$+$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{4}q^{7}+\cdots$
7605.2.a.cp	$9$	$60.726$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$-3$	$0$	$-9$	$7$	$-$	$+$	$+$	$q+(-\beta _{1}-\beta _{6})q^{2}+(2-\beta _{3}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
7605.2.a.cq	$9$	$60.726$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$0$	$0$	$-9$	$-10$	$-$	$+$	$+$	$q+\beta _{7}q^{2}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$
7605.2.a.cr	$9$	$60.726$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$0$	$0$	$9$	$10$	$-$	$-$	$-$	$q-\beta _{7}q^{2}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots$
7605.2.a.cs	$9$	$60.726$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	None	$3$	$0$	$9$	$-7$	$-$	$-$	$-$	$q+(\beta _{1}+\beta _{6})q^{2}+(2-\beta _{3}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots$
7605.2.a.ct	$10$	$60.726$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$-4$	$0$	$10$	$0$	$+$	$-$	$-$	$q-\beta _{4}q^{2}+(1+\beta _{5})q^{4}+q^{5}+\beta _{9}q^{7}+\cdots$
7605.2.a.cu	$10$	$60.726$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	$4$	$0$	$-10$	$0$	$+$	$+$	$-$	$q+\beta _{4}q^{2}+(1+\beta _{5})q^{4}-q^{5}+\beta _{9}q^{7}+\cdots$
7605.2.a.cv	$12$	$60.726$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$-1$	$0$	$12$	$-12$	$+$	$-$	$-$	$q-\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots$
7605.2.a.cw	$12$	$60.726$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$-1$	$0$	$12$	$12$	$+$	$-$	$+$	$q-\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots$
7605.2.a.cx	$12$	$60.726$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$1$	$0$	$-12$	$-12$	$+$	$+$	$-$	$q+\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots$
7605.2.a.cy	$12$	$60.726$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	$1$	$0$	$-12$	$12$	$+$	$+$	$+$	$q+\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(7605))$ into lower level spaces

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Level:	\( N \)	\(=\)	\( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7605.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 77 \)
Sturm bound:			\(2184\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

\(3\)	\(5\)	\(13\)	Fricke	Dim.
\(+\)	\(+\)	\(+\)	\(+\)	\(26\)
\(+\)	\(+\)	\(-\)	\(-\)	\(26\)
\(+\)	\(-\)	\(+\)	\(-\)	\(26\)
\(+\)	\(-\)	\(-\)	\(+\)	\(26\)
\(-\)	\(+\)	\(+\)	\(-\)	\(42\)
\(-\)	\(+\)	\(-\)	\(+\)	\(36\)
\(-\)	\(-\)	\(+\)	\(+\)	\(35\)
\(-\)	\(-\)	\(-\)	\(-\)	\(42\)
Plus space			\(+\)	\(123\)
Minus space			\(-\)	\(136\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7605))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7605))\) 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	7605.2.a

Level	$7605$
Weight	$2$
Character orbit	7605.a
Rep. character	$\chi_{7605}(1,\cdot)$
Character field	$\Q$
Dimension	$259$
Newform subspaces	$77$
Sturm bound	$2184$
Trace bound	$11$

Label	Dim.	\(A\)	Field	CM	Traces				A-L signs			$q$-expansion
Label	Dim.	\(A\)	Field	CM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	3	5	13	$q$-expansion
7605.2.a.a	\(1\)	\(60.726\)	\(\Q\)	None	\(-2\)	\(0\)	\(1\)	\(5\)	\(-\)	\(-\)	\(+\)	\(q-2q^{2}+2q^{4}+q^{5}+5q^{7}-2q^{10}+\cdots\)
7605.2.a.b	\(1\)	\(60.726\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(-4\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}-q^{4}-q^{5}-4q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.c	\(1\)	\(60.726\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(-2\)	\(+\)	\(+\)	\(+\)	\(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.d	\(1\)	\(60.726\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(2\)	\(-\)	\(+\)	\(-\)	\(q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.e	\(1\)	\(60.726\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(4\)	\(+\)	\(+\)	\(-\)	\(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.f	\(1\)	\(60.726\)	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(4\)	\(-\)	\(+\)	\(+\)	\(q-q^{2}-q^{4}-q^{5}+4q^{7}+3q^{8}+q^{10}+\cdots\)
7605.2.a.g	\(1\)	\(60.726\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}-4q^{11}+\cdots\)
7605.2.a.h	\(1\)	\(60.726\)	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q-q^{2}-q^{4}+q^{5}+3q^{8}-q^{10}+4q^{11}+\cdots\)
7605.2.a.i	\(1\)	\(60.726\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(-3\)	\(-\)	\(+\)	\(-\)	\(q-2q^{4}-q^{5}-3q^{7}-3q^{11}+4q^{16}+\cdots\)
7605.2.a.j	\(1\)	\(60.726\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(1\)	\(+\)	\(+\)	\(+\)	\(q-2q^{4}-q^{5}+q^{7}+3q^{11}+4q^{16}+\cdots\)
7605.2.a.k	\(1\)	\(60.726\)	\(\Q\)	None	\(0\)	\(0\)	\(-1\)	\(1\)	\(-\)	\(+\)	\(+\)	\(q-2q^{4}-q^{5}+q^{7}+6q^{11}+4q^{16}+\cdots\)
7605.2.a.l	\(1\)	\(60.726\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(-1\)	\(-\)	\(-\)	\(+\)	\(q-2q^{4}+q^{5}-q^{7}-6q^{11}+4q^{16}+\cdots\)
7605.2.a.m	\(1\)	\(60.726\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(1\)	\(+\)	\(-\)	\(+\)	\(q-2q^{4}+q^{5}+q^{7}-3q^{11}+4q^{16}+\cdots\)
7605.2.a.n	\(1\)	\(60.726\)	\(\Q\)	None	\(0\)	\(0\)	\(1\)	\(3\)	\(-\)	\(-\)	\(-\)	\(q-2q^{4}+q^{5}+3q^{7}+3q^{11}+4q^{16}+\cdots\)
7605.2.a.o	\(1\)	\(60.726\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(-4\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.p	\(1\)	\(60.726\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(-2\)	\(-\)	\(-\)	\(-\)	\(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.q	\(1\)	\(60.726\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(-2\)	\(+\)	\(-\)	\(+\)	\(q+q^{2}-q^{4}+q^{5}-2q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.r	\(1\)	\(60.726\)	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(4\)	\(+\)	\(-\)	\(-\)	\(q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots\)
7605.2.a.s	\(1\)	\(60.726\)	\(\Q\)	None	\(2\)	\(0\)	\(-1\)	\(-5\)	\(-\)	\(+\)	\(+\)	\(q+2q^{2}+2q^{4}-q^{5}-5q^{7}-2q^{10}+\cdots\)
7605.2.a.t	\(1\)	\(60.726\)	\(\Q\)	None	\(2\)	\(0\)	\(-1\)	\(1\)	\(-\)	\(+\)	\(+\)	\(q+2q^{2}+2q^{4}-q^{5}+q^{7}-2q^{10}+\cdots\)
7605.2.a.u	\(1\)	\(60.726\)	\(\Q\)	None	\(2\)	\(0\)	\(1\)	\(-3\)	\(-\)	\(-\)	\(+\)	\(q+2q^{2}+2q^{4}+q^{5}-3q^{7}+2q^{10}+\cdots\)
7605.2.a.v	\(1\)	\(60.726\)	\(\Q\)	None	\(2\)	\(0\)	\(1\)	\(3\)	\(-\)	\(-\)	\(+\)	\(q+2q^{2}+2q^{4}+q^{5}+3q^{7}+2q^{10}+\cdots\)
7605.2.a.w	\(2\)	\(60.726\)	\(\Q(\sqrt{13}) \)	None	\(-4\)	\(0\)	\(2\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-2q^{2}+2q^{4}+q^{5}-\beta q^{7}-2q^{10}+\cdots\)
7605.2.a.x	\(2\)	\(60.726\)	\(\Q(\sqrt{2}) \)	None	\(-2\)	\(0\)	\(2\)	\(-4\)	\(-\)	\(-\)	\(+\)	\(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots\)
7605.2.a.y	\(2\)	\(60.726\)	\(\Q(\sqrt{3}) \)	None	\(-2\)	\(0\)	\(-2\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.z	\(2\)	\(60.726\)	\(\Q(\sqrt{3}) \)	None	\(-2\)	\(0\)	\(2\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+(-1+\beta )q^{2}+(2-2\beta )q^{4}+q^{5}+\beta q^{7}+\cdots\)
7605.2.a.ba	\(2\)	\(60.726\)	\(\Q(\sqrt{5}) \)	None	\(-1\)	\(0\)	\(-2\)	\(4\)	\(-\)	\(+\)	\(+\)	\(q-\beta q^{2}+(-1+\beta )q^{4}-q^{5}+(3-2\beta )q^{7}+\cdots\)
7605.2.a.bb	\(2\)	\(60.726\)	\(\Q(\sqrt{13}) \)	None	\(-1\)	\(0\)	\(-2\)	\(2\)	\(-\)	\(+\)	\(+\)	\(q-\beta q^{2}+(1+\beta )q^{4}-q^{5}+q^{7}-3q^{8}+\cdots\)
7605.2.a.bc	\(2\)	\(60.726\)	\(\Q(\sqrt{17}) \)	None	\(-1\)	\(0\)	\(-2\)	\(-3\)	\(-\)	\(+\)	\(-\)	\(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(-1-\beta )q^{7}+\cdots\)
7605.2.a.bd	\(2\)	\(60.726\)	\(\Q(\sqrt{17}) \)	None	\(-1\)	\(0\)	\(-2\)	\(5\)	\(+\)	\(+\)	\(+\)	\(q-\beta q^{2}+(2+\beta )q^{4}-q^{5}+(3-\beta )q^{7}+\cdots\)
7605.2.a.be	\(2\)	\(60.726\)	\(\Q(\sqrt{3}) \)	None	\(0\)	\(0\)	\(-2\)	\(-4\)	\(-\)	\(+\)	\(+\)	\(q+\beta q^{2}+q^{4}-q^{5}-2q^{7}-\beta q^{8}-\beta q^{10}+\cdots\)
7605.2.a.bf	\(2\)	\(60.726\)	\(\Q(\sqrt{5}) \)	None	\(1\)	\(0\)	\(2\)	\(-4\)	\(-\)	\(-\)	\(+\)	\(q+\beta q^{2}+(-1+\beta )q^{4}+q^{5}+(-3+2\beta )q^{7}+\cdots\)
7605.2.a.bg	\(2\)	\(60.726\)	\(\Q(\sqrt{13}) \)	None	\(1\)	\(0\)	\(2\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(q+\beta q^{2}+(1+\beta )q^{4}+q^{5}-q^{7}+3q^{8}+\cdots\)
7605.2.a.bh	\(2\)	\(60.726\)	\(\Q(\sqrt{17}) \)	None	\(1\)	\(0\)	\(2\)	\(3\)	\(-\)	\(-\)	\(-\)	\(q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(1+\beta )q^{7}+\cdots\)
7605.2.a.bi	\(2\)	\(60.726\)	\(\Q(\sqrt{17}) \)	None	\(1\)	\(0\)	\(2\)	\(5\)	\(+\)	\(-\)	\(+\)	\(q+\beta q^{2}+(2+\beta )q^{4}+q^{5}+(3-\beta )q^{7}+\cdots\)
7605.2.a.bj	\(2\)	\(60.726\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(+\)	\(+\)	\(q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}+\beta q^{7}+\cdots\)
7605.2.a.bk	\(2\)	\(60.726\)	\(\Q(\sqrt{3}) \)	None	\(2\)	\(0\)	\(2\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q+(1+\beta )q^{2}+(2+2\beta )q^{4}+q^{5}+(1-2\beta )q^{7}+\cdots\)
7605.2.a.bl	\(2\)	\(60.726\)	\(\Q(\sqrt{13}) \)	None	\(4\)	\(0\)	\(-2\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+2q^{2}+2q^{4}-q^{5}+\beta q^{7}-2q^{10}+\cdots\)
7605.2.a.bm	\(3\)	\(60.726\)	\(\Q(\zeta_{14})^+\)	None	\(-3\)	\(0\)	\(3\)	\(0\)	\(-\)	\(-\)	\(+\)	\(q+(-1+\beta _{1}+\beta _{2})q^{2}+(4-\beta _{1})q^{4}+\cdots\)
7605.2.a.bn	\(3\)	\(60.726\)	\(\Q(\zeta_{14})^+\)	None	\(-2\)	\(0\)	\(-3\)	\(-4\)	\(-\)	\(+\)	\(-\)	\(q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
7605.2.a.bo	\(3\)	\(60.726\)	\(\Q(\zeta_{14})^+\)	None	\(-1\)	\(0\)	\(-3\)	\(-4\)	\(-\)	\(+\)	\(+\)	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bp	\(3\)	\(60.726\)	\(\Q(\zeta_{14})^+\)	None	\(-1\)	\(0\)	\(3\)	\(-12\)	\(-\)	\(-\)	\(+\)	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}-4q^{7}+(-1+\cdots)q^{8}+\cdots\)
7605.2.a.bq	\(3\)	\(60.726\)	\(\Q(\zeta_{14})^+\)	None	\(-1\)	\(0\)	\(3\)	\(-2\)	\(-\)	\(-\)	\(+\)	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.br	\(3\)	\(60.726\)	\(\Q(\zeta_{14})^+\)	None	\(-1\)	\(0\)	\(3\)	\(5\)	\(-\)	\(-\)	\(+\)	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(1+\beta _{1}-\beta _{2})q^{7}+\cdots\)
7605.2.a.bs	\(3\)	\(60.726\)	3.3.564.1	None	\(-1\)	\(0\)	\(3\)	\(2\)	\(-\)	\(-\)	\(-\)	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1+\beta _{2})q^{7}+\cdots\)
7605.2.a.bt	\(3\)	\(60.726\)	3.3.148.1	None	\(0\)	\(0\)	\(-3\)	\(5\)	\(-\)	\(+\)	\(+\)	\(q-\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)
7605.2.a.bu	\(3\)	\(60.726\)	3.3.148.1	None	\(0\)	\(0\)	\(3\)	\(-5\)	\(-\)	\(-\)	\(+\)	\(q+\beta _{2}q^{2}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.bv	\(3\)	\(60.726\)	3.3.756.1	None	\(0\)	\(0\)	\(-3\)	\(3\)	\(-\)	\(+\)	\(+\)	\(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bw	\(3\)	\(60.726\)	3.3.756.1	None	\(0\)	\(0\)	\(3\)	\(-3\)	\(-\)	\(-\)	\(+\)	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bx	\(3\)	\(60.726\)	3.3.316.1	None	\(0\)	\(0\)	\(-3\)	\(-1\)	\(-\)	\(+\)	\(+\)	\(q-\beta _{1}q^{2}+(3+\beta _{2})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots\)
7605.2.a.by	\(3\)	\(60.726\)	\(\Q(\zeta_{14})^+\)	None	\(1\)	\(0\)	\(-3\)	\(-5\)	\(-\)	\(+\)	\(-\)	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.bz	\(3\)	\(60.726\)	\(\Q(\zeta_{14})^+\)	None	\(1\)	\(0\)	\(-3\)	\(2\)	\(-\)	\(+\)	\(-\)	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(1-\beta _{1})q^{7}+\cdots\)
7605.2.a.ca	\(3\)	\(60.726\)	\(\Q(\zeta_{14})^+\)	None	\(1\)	\(0\)	\(-3\)	\(12\)	\(-\)	\(+\)	\(-\)	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+4q^{7}+(1-2\beta _{1}+\cdots)q^{8}+\cdots\)
7605.2.a.cb	\(3\)	\(60.726\)	\(\Q(\zeta_{14})^+\)	None	\(1\)	\(0\)	\(3\)	\(4\)	\(-\)	\(-\)	\(-\)	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(1+\beta _{1})q^{7}+\cdots\)
7605.2.a.cc	\(3\)	\(60.726\)	3.3.564.1	None	\(1\)	\(0\)	\(-3\)	\(-2\)	\(-\)	\(+\)	\(-\)	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
7605.2.a.cd	\(3\)	\(60.726\)	\(\Q(\zeta_{14})^+\)	None	\(2\)	\(0\)	\(3\)	\(4\)	\(-\)	\(-\)	\(+\)	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
7605.2.a.ce	\(3\)	\(60.726\)	\(\Q(\zeta_{14})^+\)	None	\(3\)	\(0\)	\(-3\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+(1-\beta _{1}-\beta _{2})q^{2}+(4-\beta _{1})q^{4}-q^{5}+\cdots\)
7605.2.a.cf	\(4\)	\(60.726\)	4.4.4752.1	None	\(-2\)	\(0\)	\(4\)	\(10\)	\(-\)	\(-\)	\(-\)	\(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+(3+\beta _{2}+\cdots)q^{7}+\cdots\)
7605.2.a.cg	\(4\)	\(60.726\)	4.4.7488.1	None	\(-2\)	\(0\)	\(-4\)	\(6\)	\(-\)	\(+\)	\(-\)	\(q+\beta _{3}q^{2}+(1-\beta _{2})q^{4}-q^{5}+(2-\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.ch	\(4\)	\(60.726\)	4.4.13824.1	None	\(0\)	\(0\)	\(-4\)	\(0\)	\(-\)	\(+\)	\(-\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
7605.2.a.ci	\(4\)	\(60.726\)	4.4.13824.1	None	\(0\)	\(0\)	\(4\)	\(0\)	\(-\)	\(-\)	\(-\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
7605.2.a.cj	\(4\)	\(60.726\)	4.4.4752.1	None	\(2\)	\(0\)	\(-4\)	\(-10\)	\(-\)	\(+\)	\(-\)	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+(-3+\cdots)q^{7}+\cdots\)
7605.2.a.ck	\(4\)	\(60.726\)	4.4.7488.1	None	\(2\)	\(0\)	\(4\)	\(-6\)	\(-\)	\(-\)	\(-\)	\(q-\beta _{3}q^{2}+(1-\beta _{2})q^{4}+q^{5}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
7605.2.a.cl	\(5\)	\(60.726\)	5.5.3352656.1	None	\(-2\)	\(0\)	\(-5\)	\(-1\)	\(+\)	\(+\)	\(+\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}-\beta _{4}q^{7}+\cdots\)
7605.2.a.cm	\(5\)	\(60.726\)	5.5.3352656.1	None	\(-2\)	\(0\)	\(-5\)	\(1\)	\(+\)	\(+\)	\(+\)	\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+\beta _{4}q^{7}+\cdots\)
7605.2.a.cn	\(5\)	\(60.726\)	5.5.3352656.1	None	\(2\)	\(0\)	\(5\)	\(-1\)	\(+\)	\(-\)	\(+\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}-\beta _{4}q^{7}+\cdots\)
7605.2.a.co	\(5\)	\(60.726\)	5.5.3352656.1	None	\(2\)	\(0\)	\(5\)	\(1\)	\(+\)	\(-\)	\(+\)	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+\beta _{4}q^{7}+\cdots\)
7605.2.a.cp	\(9\)	\(60.726\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(-3\)	\(0\)	\(-9\)	\(7\)	\(-\)	\(+\)	\(+\)	\(q+(-\beta _{1}-\beta _{6})q^{2}+(2-\beta _{3}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
7605.2.a.cq	\(9\)	\(60.726\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(0\)	\(0\)	\(-9\)	\(-10\)	\(-\)	\(+\)	\(+\)	\(q+\beta _{7}q^{2}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
7605.2.a.cr	\(9\)	\(60.726\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(0\)	\(0\)	\(9\)	\(10\)	\(-\)	\(-\)	\(-\)	\(q-\beta _{7}q^{2}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
7605.2.a.cs	\(9\)	\(60.726\)	\(\mathbb{Q}[x]/(x^{9} - \cdots)\)	None	\(3\)	\(0\)	\(9\)	\(-7\)	\(-\)	\(-\)	\(-\)	\(q+(\beta _{1}+\beta _{6})q^{2}+(2-\beta _{3}-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
7605.2.a.ct	\(10\)	\(60.726\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(-4\)	\(0\)	\(10\)	\(0\)	\(+\)	\(-\)	\(-\)	\(q-\beta _{4}q^{2}+(1+\beta _{5})q^{4}+q^{5}+\beta _{9}q^{7}+\cdots\)
7605.2.a.cu	\(10\)	\(60.726\)	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None	\(4\)	\(0\)	\(-10\)	\(0\)	\(+\)	\(+\)	\(-\)	\(q+\beta _{4}q^{2}+(1+\beta _{5})q^{4}-q^{5}+\beta _{9}q^{7}+\cdots\)
7605.2.a.cv	\(12\)	\(60.726\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(-1\)	\(0\)	\(12\)	\(-12\)	\(+\)	\(-\)	\(-\)	\(q-\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}+q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.cw	\(12\)	\(60.726\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(-1\)	\(0\)	\(12\)	\(12\)	\(+\)	\(-\)	\(+\)	\(q-\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots\)
7605.2.a.cx	\(12\)	\(60.726\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(1\)	\(0\)	\(-12\)	\(-12\)	\(+\)	\(+\)	\(-\)	\(q+\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
7605.2.a.cy	\(12\)	\(60.726\)	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	\(1\)	\(0\)	\(-12\)	\(12\)	\(+\)	\(+\)	\(+\)	\(q+\beta _{1}q^{2}+(1-\beta _{3}+\beta _{4})q^{4}-q^{5}+(1+\cdots)q^{7}+\cdots\)