Space of modular forms of level 2664, weight 2, and Character 2664.h

• Label: 2664.2.h
• Level: $2664$
• Weight: $2$
• Character orbit: 2664.h
• Rep. character: $\chi_{2664}(73,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $5$
• Sturm bound: $912$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2664 = 2^{3} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2664.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(912\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2664, [\chi])\).

	Total	New	Old
Modular forms	472	48	424
Cusp forms	440	48	392
Eisenstein series	32	0	32

Trace form

\( 48 q + 4 q^{7} - 10 q^{11} - 54 q^{25} - 4 q^{37} - 10 q^{41} + 8 q^{47} + 28 q^{49} - 8 q^{53} + 12 q^{65} + 6 q^{67} + 28 q^{71} - 2 q^{73} - 16 q^{77} + 20 q^{83} - 16 q^{85} - 36 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2664, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2664.2.h.a	$2664$	$2$	2664.h	37.b	$2$	$2$	$2$	$21.272$	\(\Q(\sqrt{-1}) \)	None					888.2.h.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-4 q^{11}+2\beta q^{13}+2\beta q^{17}-\beta q^{19}+\cdots\)
2664.2.h.b	$2664$	$2$	2664.h	37.b	$2$	$6$	$6$	$21.272$	6.0.27206656.1	None					888.2.h.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+(1-\beta _{1})q^{7}+(1+\beta _{1})q^{11}+\cdots\)
2664.2.h.c	$2664$	$2$	2664.h	37.b	$2$	$10$	$10$	$21.272$	10.0.\(\cdots\).1	None					296.2.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{5}-\beta _{3}q^{7}-\beta _{5}q^{11}+\beta _{4}q^{13}+\cdots\)
2664.2.h.d	$2664$	$2$	2664.h	37.b	$2$	$10$	$10$	$21.272$	10.0.\(\cdots\).1	None					888.2.h.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}-\beta _{3}q^{7}+(-1+\beta _{1})q^{11}+\cdots\)
2664.2.h.e	$2664$	$2$	2664.h	37.b	$2$	$20$	$20$	$21.272$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		2664.2.h.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{30}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{5}+\beta _{1}q^{7}+\beta _{10}q^{11}-\beta _{12}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2664, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2664, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(444, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(666, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(888, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1332, [\chi])\)\(^{\oplus 2}\)