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

• Label: 2304.2.d
• Level: $2304$
• Weight: $2$
• Character orbit: 2304.d
• Rep. character: $\chi_{2304}(1153,\cdot)$
• Character field: $\Q$
• Dimension: $38$
• Newform subspaces: $19$
• Sturm bound: $768$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2304.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 19 \)
Sturm bound:			\(768\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(17\), \(23\)

Dimensions

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

	Total	New	Old
Modular forms	432	42	390
Cusp forms	336	38	298
Eisenstein series	96	4	92

Trace form

\( 38 q + 4 q^{17} - 26 q^{25} - 4 q^{41} - 10 q^{49} + 40 q^{65} + 20 q^{73} - 20 q^{89} - 36 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2304.2.d.a	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)					36.2.a.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-4 q^{7}-\beta q^{13}+4\beta q^{19}+5 q^{25}+\cdots\)
2304.2.d.b	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					128.2.a.a	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-4 q^{7}+\beta q^{11}+\beta q^{13}+2 q^{17}+\cdots\)
2304.2.d.c	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					96.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-4 q^{7}-2\beta q^{11}-\beta q^{13}+\cdots\)
2304.2.d.d	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					384.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2 q^{7}+2\beta q^{11}-3\beta q^{13}-6 q^{17}+\cdots\)
2304.2.d.e	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					1152.2.a.d	$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2 q^{7}+2\beta q^{11}+\beta q^{13}+\cdots\)
2304.2.d.f	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					384.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}-2 q^{7}-2\beta q^{11}-\beta q^{13}+\cdots\)
2304.2.d.g	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					1152.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2 q^{7}+2\beta q^{11}-\beta q^{13}+\cdots\)
2304.2.d.h	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					288.2.a.a	$4$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2\beta q^{5}-3\beta q^{13}-8 q^{17}-11 q^{25}+\cdots\)
2304.2.d.i	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					24.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}-2\beta q^{11}+\beta q^{13}-2 q^{17}+\cdots\)
2304.2.d.j	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					32.2.a.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{5}-3\beta q^{13}-2 q^{17}+q^{25}+\cdots\)
2304.2.d.k	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					24.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+2\beta q^{11}+\beta q^{13}-2 q^{17}+\cdots\)
2304.2.d.l	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)					288.2.a.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+2\beta q^{5}+3\beta q^{13}+8 q^{17}-11 q^{25}+\cdots\)
2304.2.d.m	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					384.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{7}-2\beta q^{11}-3\beta q^{13}-6 q^{17}+\cdots\)
2304.2.d.n	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					1152.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+2 q^{7}-2\beta q^{11}+\beta q^{13}+\cdots\)
2304.2.d.o	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					384.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+2\beta q^{5}+2 q^{7}+2\beta q^{11}-\beta q^{13}+\cdots\)
2304.2.d.p	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					1152.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+2 q^{7}-2\beta q^{11}-\beta q^{13}+\cdots\)
2304.2.d.q	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \)					36.2.a.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+4 q^{7}-\beta q^{13}-4\beta q^{19}+5 q^{25}+\cdots\)
2304.2.d.r	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					128.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+4 q^{7}-\beta q^{11}+\beta q^{13}+2 q^{17}+\cdots\)
2304.2.d.s	$2304$	$2$	2304.d	8.b	$2$	$2$	$2$	$18.398$	\(\Q(\sqrt{-1}) \)	None					96.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+4 q^{7}+2\beta q^{11}-\beta q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2304, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)