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

• Label: 2304.3.h
• Level: $2304$
• Weight: $3$
• Character orbit: 2304.h
• Rep. character: $\chi_{2304}(2177,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $12$
• Sturm bound: $1152$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2304.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(1152\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	816	64	752
Cusp forms	720	64	656
Eisenstein series	96	0	96

Trace form

\( 64 q + 320 q^{25} + 320 q^{49} - 640 q^{73} - 896 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2304.3.h.a	$2304$	$3$	2304.h	24.h	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{8})\)	None					72.3.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-48\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-5\beta_{3} q^{5}-12 q^{7}+4\beta_{3} q^{11}-4\beta_1 q^{13}+\cdots\)
2304.3.h.b	$2304$	$3$	2304.h	24.h	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{8})\)	None					288.3.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-32\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{5}-8 q^{7}+8\beta_{3} q^{11}-4\beta_1 q^{13}+\cdots\)
2304.3.h.c	$2304$	$3$	2304.h	24.h	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{8})\)	None					18.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{5}-4 q^{7}+4\beta_{3} q^{11}+4\beta_1 q^{13}+\cdots\)
2304.3.h.d	$2304$	$3$	2304.h	24.h	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)					288.3.e.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta_{3} q^{5}+12\beta_1 q^{13}+23\beta_{2} q^{17}+\cdots\)
2304.3.h.e	$2304$	$3$	2304.h	24.h	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-1}) \)					288.3.e.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-7\beta_{3} q^{5}+12\beta_1 q^{13}-7\beta_{2} q^{17}+\cdots\)
2304.3.h.f	$2304$	$3$	2304.h	24.h	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{8})\)	None					18.3.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{5}+4 q^{7}-4\beta_{3} q^{11}+4\beta_1 q^{13}+\cdots\)
2304.3.h.g	$2304$	$3$	2304.h	24.h	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{8})\)	None					288.3.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(32\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{3} q^{5}+8 q^{7}-8\beta_{3} q^{11}+4\beta_1 q^{13}+\cdots\)
2304.3.h.h	$2304$	$3$	2304.h	24.h	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{8})\)	None					72.3.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(48\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+5\beta_{3} q^{5}+12 q^{7}+4\beta_{3} q^{11}-4\beta_1 q^{13}+\cdots\)
2304.3.h.i	$2304$	$3$	2304.h	24.h	$2$	$8$	$8$	$62.779$	\(\Q(\zeta_{24})\)	None					1152.3.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{5}+\beta_{3})q^{5}+(\beta_{7}-2)q^{7}+(2\beta_{5}+2\beta_{3})q^{11}+\cdots\)
2304.3.h.j	$2304$	$3$	2304.h	24.h	$2$	$8$	$8$	$62.779$	\(\Q(i, \sqrt{2}, \sqrt{11})\)	None					1152.3.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{5}-2q^{7}+(-4\beta _{3}+2\beta _{5}+\cdots)q^{11}+\cdots\)
2304.3.h.k	$2304$	$3$	2304.h	24.h	$2$	$8$	$8$	$62.779$	\(\Q(\zeta_{24})\)	None					1152.3.e.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{5}+\beta_{3})q^{5}+(-\beta_{7}+2)q^{7}+(-2\beta_{5}-2\beta_{3})q^{11}+\cdots\)
2304.3.h.l	$2304$	$3$	2304.h	24.h	$2$	$8$	$8$	$62.779$	\(\Q(i, \sqrt{2}, \sqrt{11})\)	None					1152.3.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{3}+\beta _{5})q^{5}+2q^{7}+(-4\beta _{3}+2\beta _{5}+\cdots)q^{11}+\cdots\)

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

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