Space of modular forms of level 2304, weight 3, and Character 2304.b

• Label: 2304.3.b
• Level: $2304$
• Weight: $3$
• Character orbit: 2304.b
• Rep. character: $\chi_{2304}(127,\cdot)$
• Character field: $\Q$
• Dimension: $78$
• Newform subspaces: $20$
• Sturm bound: $1152$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2304.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(1152\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2304, [\chi])\).

	Total	New	Old
Modular forms	816	82	734
Cusp forms	720	78	642
Eisenstein series	96	4	92

Trace form

\( 78 q + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2304, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2304.3.b.a	$2304$	$3$	2304.b	8.d	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}-2iq^{7}-2^{4}q^{11}-iq^{13}+\cdots\)
2304.3.b.b	$2304$	$3$	2304.b	8.d	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}-2iq^{7}-2^{4}q^{11}+iq^{13}+\cdots\)
2304.3.b.c	$2304$	$3$	2304.b	8.d	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}-4iq^{7}-4q^{11}-7iq^{13}+\cdots\)
2304.3.b.d	$2304$	$3$	2304.b	8.d	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+4iq^{5}+5iq^{13}-2^{4}q^{17}-39q^{25}+\cdots\)
2304.3.b.e	$2304$	$3$	2304.b	8.d	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+4iq^{5}-5iq^{13}+2^{4}q^{17}-39q^{25}+\cdots\)
2304.3.b.f	$2304$	$3$	2304.b	8.d	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+3iq^{5}-5iq^{13}+30q^{17}-11q^{25}+\cdots\)
2304.3.b.g	$2304$	$3$	2304.b	8.d	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{5}+4iq^{7}+4q^{11}-7iq^{13}+\cdots\)
2304.3.b.h	$2304$	$3$	2304.b	8.d	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}+2iq^{7}+2^{4}q^{11}-iq^{13}+\cdots\)
2304.3.b.i	$2304$	$3$	2304.b	8.d	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{5}+2iq^{7}+2^{4}q^{11}+iq^{13}+\cdots\)
2304.3.b.j	$2304$	$3$	2304.b	8.d	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{3})q^{5}+(-2\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots\)
2304.3.b.k	$2304$	$3$	2304.b	8.d	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{5}+(-2\zeta_{12}+\zeta_{12}^{3})q^{7}+\cdots\)
2304.3.b.l	$2304$	$3$	2304.b	8.d	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
2304.3.b.m	$2304$	$3$	2304.b	8.d	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{12}^{2}q^{7}-11\zeta_{12}q^{13}-\zeta_{12}^{3}q^{19}+\cdots\)
2304.3.b.n	$2304$	$3$	2304.b	8.d	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3\zeta_{12}q^{5}+\zeta_{12}^{3}q^{7}-3\zeta_{12}^{2}q^{11}+\cdots\)
2304.3.b.o	$2304$	$3$	2304.b	8.d	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{12}-\zeta_{12}^{3})q^{5}+(2\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots\)
2304.3.b.p	$2304$	$3$	2304.b	8.d	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{3})q^{5}+(2\zeta_{8}-\zeta_{8}^{3})q^{7}+(10+\cdots)q^{11}+\cdots\)
2304.3.b.q	$2304$	$3$	2304.b	8.d	$2$	$8$	$8$	$62.779$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{24}-\zeta_{24}^{3})q^{5}+(\zeta_{24}+\zeta_{24}^{3}+\zeta_{24}^{6}+\cdots)q^{7}+\cdots\)
2304.3.b.r	$2304$	$3$	2304.b	8.d	$2$	$8$	$8$	$62.779$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+(\beta _{1}+\beta _{6})q^{7}-\beta _{4}q^{11}+(3\beta _{1}+\cdots)q^{13}+\cdots\)
2304.3.b.s	$2304$	$3$	2304.b	8.d	$2$	$8$	$8$	$62.779$	8.0.157351936.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{5}+(-\beta _{1}-\beta _{6})q^{7}+\beta _{4}q^{11}+\cdots\)
2304.3.b.t	$2304$	$3$	2304.b	8.d	$2$	$8$	$8$	$62.779$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{24}-\zeta_{24}^{3})q^{5}+(-\zeta_{24}-\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(2304, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)