Space of modular forms of level 7436, weight 2, and trivial character

• Label: 7436.2.a
• Level: $7436$
• Weight: $2$
• Character orbit: 7436.a
• Rep. character: $\chi_{7436}(1,\cdot)$
• Character field: $\Q$
• Dimension: $129$
• Newform subspaces: $24$
• Sturm bound: $2184$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 7436 = 2^{2} \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7436.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 24 \)
Sturm bound:			\(2184\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7436))\).

	Total	New	Old
Modular forms	1134	129	1005
Cusp forms	1051	129	922
Eisenstein series	83	0	83

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

\(2\)	\(11\)	\(13\)	Fricke	Dim
\(-\)	\(+\)	\(+\)	$-$	\(34\)
\(-\)	\(+\)	\(-\)	$+$	\(31\)
\(-\)	\(-\)	\(+\)	$+$	\(27\)
\(-\)	\(-\)	\(-\)	$-$	\(37\)
Plus space			\(+\)	\(58\)
Minus space			\(-\)	\(71\)

Trace form

\( 129 q + q^{3} + q^{5} - 2 q^{7} + 126 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7436))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs			Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	11	13
7436.2.a.a	$7436$	$2$	7436.a	1.a	$1$	$1$	$1$	$59.377$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-4q^{7}-3q^{9}+q^{11}+2q^{17}+4q^{19}+\cdots\)
7436.2.a.b	$7436$	$2$	7436.a	1.a	$1$	$1$	$1$	$59.377$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(0\)	\(0\)	\(4\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+4q^{7}-3q^{9}-q^{11}+2q^{17}-4q^{19}+\cdots\)
7436.2.a.c	$7436$	$2$	7436.a	1.a	$1$	$1$	$1$	$59.377$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(1\)	\(-3\)	\(-2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}-3q^{5}-2q^{7}-2q^{9}-q^{11}+\cdots\)
7436.2.a.d	$7436$	$2$	7436.a	1.a	$1$	$1$	$1$	$59.377$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(1\)	\(3\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+q^{3}+3q^{5}-2q^{7}-2q^{9}+q^{11}+\cdots\)
7436.2.a.e	$7436$	$2$	7436.a	1.a	$1$	$2$	$2$	$59.377$	\(\Q(\sqrt{13}) \)	None	✓	$1$	$1$	\(0\)	\(-3\)	\(0\)	\(3\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta )q^{3}+(2-\beta )q^{7}+(1+3\beta )q^{9}+\cdots\)
7436.2.a.f	$7436$	$2$	7436.a	1.a	$1$	$2$	$2$	$59.377$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$0$	\(0\)	\(-2\)	\(-2\)	\(2\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}-q^{5}+(1-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
7436.2.a.g	$7436$	$2$	7436.a	1.a	$1$	$2$	$2$	$59.377$	\(\Q(\sqrt{3}) \)	None	✓	$1$	$1$	\(0\)	\(-2\)	\(2\)	\(-2\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta )q^{3}+q^{5}+(-1+\beta )q^{7}+\cdots\)
7436.2.a.h	$7436$	$2$	7436.a	1.a	$1$	$2$	$2$	$59.377$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(-4\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}-2q^{5}+(-3+\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
7436.2.a.i	$7436$	$2$	7436.a	1.a	$1$	$2$	$2$	$59.377$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$1$	\(0\)	\(1\)	\(0\)	\(-3\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(-1-\beta )q^{7}+(2+\beta )q^{9}-q^{11}+\cdots\)
7436.2.a.j	$7436$	$2$	7436.a	1.a	$1$	$2$	$2$	$59.377$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(0\)	\(3\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+(1+\beta )q^{7}+(2+\beta )q^{9}+q^{11}+\cdots\)
7436.2.a.k	$7436$	$2$	7436.a	1.a	$1$	$2$	$2$	$59.377$	\(\Q(\sqrt{21}) \)	None	✓	$1$	$0$	\(0\)	\(1\)	\(4\)	\(-3\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta q^{3}+2q^{5}+(-1-\beta )q^{7}+(2+\beta )q^{9}+\cdots\)
7436.2.a.l	$7436$	$2$	7436.a	1.a	$1$	$3$	$3$	$59.377$	3.3.229.1	None	✓	$1$	$0$	\(0\)	\(-2\)	\(1\)	\(7\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+(-1-\beta _{2})q^{3}+(-\beta _{1}-\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots\)
7436.2.a.m	$7436$	$2$	7436.a	1.a	$1$	$3$	$3$	$59.377$	3.3.321.1	None	✓	$1$	$1$	\(0\)	\(1\)	\(-3\)	\(-5\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
7436.2.a.n	$7436$	$2$	7436.a	1.a	$1$	$3$	$3$	$59.377$	3.3.321.1	None	✓	$1$	$0$	\(0\)	\(1\)	\(3\)	\(5\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
7436.2.a.o	$7436$	$2$	7436.a	1.a	$1$	$4$	$4$	$59.377$	4.4.114024.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(0\)	\(-5\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}-\beta _{2}q^{5}+(-1-\beta _{1})q^{7}+(2+\cdots)q^{9}+\cdots\)
7436.2.a.p	$7436$	$2$	7436.a	1.a	$1$	$4$	$4$	$59.377$	4.4.114024.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(0\)	\(5\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(1+\beta _{1})q^{7}+(2+\beta _{1}+\cdots)q^{9}+\cdots\)
7436.2.a.q	$7436$	$2$	7436.a	1.a	$1$	$5$	$5$	$59.377$	5.5.1020732.1	None	✓	$1$	$0$	\(0\)	\(-1\)	\(-1\)	\(1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2}-\beta _{4})q^{5}+\beta _{2}q^{7}+\cdots\)
7436.2.a.r	$7436$	$2$	7436.a	1.a	$1$	$5$	$5$	$59.377$	5.5.1020732.1	None	✓	$1$	$1$	\(0\)	\(-1\)	\(1\)	\(-1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\beta _{4})q^{5}-\beta _{2}q^{7}+\cdots\)
7436.2.a.s	$7436$	$2$	7436.a	1.a	$1$	$12$	$12$	$59.377$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-6\)	\(-5\)	\(1\)		$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}+\beta _{4}q^{5}+(-\beta _{3}-\beta _{6}+\cdots)q^{7}+\cdots\)
7436.2.a.t	$7436$	$2$	7436.a	1.a	$1$	$12$	$12$	$59.377$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-6\)	\(5\)	\(-1\)		$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{3}-\beta _{4}q^{5}+(\beta _{3}+\beta _{6}+\cdots)q^{7}+\cdots\)
7436.2.a.u	$7436$	$2$	7436.a	1.a	$1$	$12$	$12$	$59.377$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(2\)	\(0\)	\(-8\)		$-$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{7}q^{5}+(-1-\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots\)
7436.2.a.v	$7436$	$2$	7436.a	1.a	$1$	$12$	$12$	$59.377$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(2\)	\(0\)	\(8\)		$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{7}q^{5}+(1+\beta _{3})q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
7436.2.a.w	$7436$	$2$	7436.a	1.a	$1$	$18$	$18$	$59.377$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(7\)	\(-8\)	\(-1\)		$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}+\beta _{9}q^{5}+\beta _{14}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
7436.2.a.x	$7436$	$2$	7436.a	1.a	$1$	$18$	$18$	$59.377$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(7\)	\(8\)	\(1\)		$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{3}-\beta _{9}q^{5}-\beta _{14}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7436))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7436)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1859))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3718))\)\(^{\oplus 2}\)