Space of modular forms of level 7644, weight 2, and Character 7644.e

• Label: 7644.2.e
• Level: $7644$
• Weight: $2$
• Character orbit: 7644.e
• Rep. character: $\chi_{7644}(4705,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $17$
• Sturm bound: $3136$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 7644 = 2^{2} \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7644.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 17 \)
Sturm bound:			\(3136\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7644, [\chi])\).

	Total	New	Old
Modular forms	1616	96	1520
Cusp forms	1520	96	1424
Eisenstein series	96	0	96

Trace form

\( 96 q + 96 q^{9} + 4 q^{13} - 8 q^{23} - 88 q^{25} - 8 q^{29} + 14 q^{39} + 12 q^{43} + 8 q^{51} + 72 q^{53} - 32 q^{55} + 8 q^{61} + 36 q^{65} + 8 q^{69} - 16 q^{75} - 68 q^{79} + 96 q^{81} - 8 q^{87} - 24 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(7644, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
7644.2.e.a	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	\(\Q(\sqrt{-1}) \)	None					1092.2.cu.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+2 i q^{5}+q^{9}-i q^{11}+(-2 i-3)q^{13}+\cdots\)
7644.2.e.b	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	\(\Q(\sqrt{-1}) \)	None					156.2.b.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta q^{5}+q^{9}+3\beta q^{11}+(-\beta-3)q^{13}+\cdots\)
7644.2.e.c	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	\(\Q(\sqrt{-1}) \)	None					1092.2.e.d	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+i q^{5}+q^{9}+(3 i-2)q^{13}+\cdots\)
7644.2.e.d	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	\(\Q(\sqrt{-1}) \)	None					1092.2.e.c	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+q^{9}-2\beta q^{11}+(-\beta+3)q^{13}+\cdots\)
7644.2.e.e	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	\(\Q(\sqrt{-1}) \)	None					1092.2.e.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+2\beta q^{5}+q^{9}+(\beta+3)q^{13}+\cdots\)
7644.2.e.f	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	\(\Q(\sqrt{-1}) \)	None					1092.2.e.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta q^{5}+q^{9}-\beta q^{11}+(-\beta-3)q^{13}+\cdots\)
7644.2.e.g	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	\(\Q(\sqrt{-3}) \)	None					156.2.b.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta q^{5}+q^{9}+\beta q^{11}+(-\beta+1)q^{13}+\cdots\)
7644.2.e.h	$7644$	$2$	7644.e	13.b	$2$	$2$	$2$	$61.038$	\(\Q(\sqrt{-1}) \)	None					1092.2.cu.a	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+2 i q^{5}+q^{9}+i q^{11}+(-2 i+3)q^{13}+\cdots\)
7644.2.e.i	$7644$	$2$	7644.e	13.b	$2$	$4$	$4$	$61.038$	\(\Q(i, \sqrt{17})\)	None					1092.2.e.e	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(-\beta _{1}-\beta _{2})q^{5}+q^{9}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
7644.2.e.j	$7644$	$2$	7644.e	13.b	$2$	$6$	$6$	$61.038$	6.0.50922496.1	None		✓			7644.2.e.j	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{1}q^{5}+q^{9}+\beta _{4}q^{11}+(-1+\cdots)q^{13}+\cdots\)
7644.2.e.k	$7644$	$2$	7644.e	13.b	$2$	$6$	$6$	$61.038$	6.0.3375599808.1	None					1092.2.cu.b	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{1}q^{5}+q^{9}+\beta _{5}q^{11}+(1-\beta _{1}+\cdots)q^{13}+\cdots\)
7644.2.e.l	$7644$	$2$	7644.e	13.b	$2$	$6$	$6$	$61.038$	6.0.3375599808.1	None					1092.2.cu.b	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{1}q^{5}+q^{9}-\beta _{5}q^{11}+(-1+\cdots)q^{13}+\cdots\)
7644.2.e.m	$7644$	$2$	7644.e	13.b	$2$	$6$	$6$	$61.038$	6.0.50922496.1	None		✓			7644.2.e.j	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta _{1}q^{5}+q^{9}-\beta _{4}q^{11}+(1-\beta _{2}+\cdots)q^{13}+\cdots\)
7644.2.e.n	$7644$	$2$	7644.e	13.b	$2$	$10$	$10$	$61.038$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					1092.2.cu.c	$2$	$0$	\(0\)	\(-10\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{1}q^{5}+q^{9}+\beta _{9}q^{11}-\beta _{5}q^{13}+\cdots\)
7644.2.e.o	$7644$	$2$	7644.e	13.b	$2$	$10$	$10$	$61.038$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None					1092.2.cu.c	$2$	$0$	\(0\)	\(10\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{1}q^{5}+q^{9}-\beta _{9}q^{11}-\beta _{6}q^{13}+\cdots\)
7644.2.e.p	$7644$	$2$	7644.e	13.b	$2$	$16$	$16$	$61.038$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			7644.2.e.p	$2$	$0$	\(0\)	\(-16\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{1}q^{5}+q^{9}-\beta _{7}q^{11}+\beta _{11}q^{13}+\cdots\)
7644.2.e.q	$7644$	$2$	7644.e	13.b	$2$	$16$	$16$	$61.038$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓			7644.2.e.p	$2$	$0$	\(0\)	\(16\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{1}q^{5}+q^{9}+\beta _{7}q^{11}+\beta _{10}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(7644, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7644, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(364, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1092, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1274, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1911, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2548, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3822, [\chi])\)\(^{\oplus 2}\)