Space of modular forms of level 2304, weight 2, and Character 2304.l

• Label: 2304.2.l
• Level: $2304$
• Weight: $2$
• Character orbit: 2304.l
• Rep. character: $\chi_{2304}(575,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $64$
• Newform subspaces: $8$
• Sturm bound: $768$
• Trace bound: $37$

Defining parameters

Level:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2304.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(768\)
Trace bound:			\(37\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2304, [\chi])\).

	Total	New	Old
Modular forms	864	64	800
Cusp forms	672	64	608
Eisenstein series	192	0	192

Trace form

\( 64 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2304, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2304.2.l.a	$2304$	$2$	2304.l	48.k	$4$	$8$	$4$	$18.398$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{1}-\beta _{4})q^{5}+(-\beta _{1}+\beta _{7})q^{7}+\cdots\)
2304.2.l.b	$2304$	$2$	2304.l	48.k	$4$	$8$	$4$	$18.398$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{6})q^{5}+\zeta_{24}^{6}q^{7}+\cdots\)
2304.2.l.c	$2304$	$2$	2304.l	48.k	$4$	$8$	$4$	$18.398$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{6})q^{5}+\zeta_{24}^{6}q^{7}+\cdots\)
2304.2.l.d	$2304$	$2$	2304.l	48.k	$4$	$8$	$4$	$18.398$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}+\beta _{7})q^{7}+\cdots\)
2304.2.l.e	$2304$	$2$	2304.l	48.k	$4$	$8$	$4$	$18.398$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{1}-\beta _{3})q^{5}+(\beta _{1}-\beta _{7})q^{7}+(1+\cdots)q^{11}+\cdots\)
2304.2.l.f	$2304$	$2$	2304.l	48.k	$4$	$8$	$4$	$18.398$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{6})q^{5}-\zeta_{24}^{6}q^{7}+\cdots\)
2304.2.l.g	$2304$	$2$	2304.l	48.k	$4$	$8$	$4$	$18.398$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\zeta_{24}-\zeta_{24}^{4}+\zeta_{24}^{6})q^{5}-\zeta_{24}^{6}q^{7}+\cdots\)
2304.2.l.h	$2304$	$2$	2304.l	48.k	$4$	$8$	$4$	$18.398$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{1}-\beta _{4})q^{5}+(\beta _{1}-\beta _{7})q^{7}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2304, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)