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

• Label: 2304.3.g
• Level: $2304$
• Weight: $3$
• Character orbit: 2304.g
• Rep. character: $\chi_{2304}(1279,\cdot)$
• Character field: $\Q$
• Dimension: $78$
• Newform subspaces: $26$
• Sturm bound: $1152$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 2304 = 2^{8} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2304.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 26 \)
Sturm bound:			\(1152\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(7\), \(11\), \(13\)

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.g.a	$2304$	$3$	2304.g	4.b	$2$	$1$	$1$	$62.779$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-8q^{5}-24q^{13}-30q^{17}+39q^{25}+\cdots\)
2304.3.g.b	$2304$	$3$	2304.g	4.b	$2$	$1$	$1$	$62.779$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-6q^{5}-24q^{13}+2^{4}q^{17}+11q^{25}+\cdots\)
2304.3.g.c	$2304$	$3$	2304.g	4.b	$2$	$1$	$1$	$62.779$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-6q^{5}+24q^{13}-2^{4}q^{17}+11q^{25}+\cdots\)
2304.3.g.d	$2304$	$3$	2304.g	4.b	$2$	$1$	$1$	$62.779$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+6q^{5}-24q^{13}-2^{4}q^{17}+11q^{25}+\cdots\)
2304.3.g.e	$2304$	$3$	2304.g	4.b	$2$	$1$	$1$	$62.779$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+6q^{5}+24q^{13}+2^{4}q^{17}+11q^{25}+\cdots\)
2304.3.g.f	$2304$	$3$	2304.g	4.b	$2$	$1$	$1$	$62.779$	\(\Q\)	\(\Q(\sqrt{-1}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+8q^{5}+24q^{13}-30q^{17}+39q^{25}+\cdots\)
2304.3.g.g	$2304$	$3$	2304.g	4.b	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-4q^{5}-\zeta_{6}q^{7}+\zeta_{6}q^{11}+18q^{17}+\cdots\)
2304.3.g.h	$2304$	$3$	2304.g	4.b	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-4q^{5}-4\beta q^{7}+5\beta q^{11}+20q^{13}+\cdots\)
2304.3.g.i	$2304$	$3$	2304.g	4.b	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{-6}) \)		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{5}-\beta q^{7}+2\beta q^{11}-21q^{25}+\cdots\)
2304.3.g.j	$2304$	$3$	2304.g	4.b	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-7iq^{11}-2q^{17}+17iq^{19}-5^{2}q^{25}+\cdots\)
2304.3.g.k	$2304$	$3$	2304.g	4.b	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-2}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta q^{11}+2q^{17}+\beta q^{19}-5^{2}q^{25}+\cdots\)
2304.3.g.l	$2304$	$3$	2304.g	4.b	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-6}) \)	\(\Q(\sqrt{-6}) \)		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{5}-\beta q^{7}-2\beta q^{11}-21q^{25}+\cdots\)
2304.3.g.m	$2304$	$3$	2304.g	4.b	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-2}) \)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+4q^{5}-4\beta q^{7}-5\beta q^{11}-20q^{13}+\cdots\)
2304.3.g.n	$2304$	$3$	2304.g	4.b	$2$	$2$	$2$	$62.779$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+4q^{5}-\zeta_{6}q^{7}-\zeta_{6}q^{11}+18q^{17}+\cdots\)
2304.3.g.o	$2304$	$3$	2304.g	4.b	$2$	$4$	$4$	$62.779$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-4+\beta _{2})q^{5}+\beta _{1}q^{7}+(4\beta _{1}-\beta _{3})q^{11}+\cdots\)
2304.3.g.p	$2304$	$3$	2304.g	4.b	$2$	$4$	$4$	$62.779$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+\beta _{1}q^{7}+\beta _{2}q^{11}-4q^{13}+\cdots\)
2304.3.g.q	$2304$	$3$	2304.g	4.b	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{2}q^{5}-5\zeta_{12}q^{7}+2\zeta_{12}^{3}q^{11}+\cdots\)
2304.3.g.r	$2304$	$3$	2304.g	4.b	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
2304.3.g.s	$2304$	$3$	2304.g	4.b	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{13}-\zeta_{12}^{3}q^{19}+\cdots\)
2304.3.g.t	$2304$	$3$	2304.g	4.b	$2$	$4$	$4$	$62.779$	\(\Q(i, \sqrt{6})\)	\(\Q(\sqrt{-6}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{5}-5\beta _{1}q^{7}+\beta _{3}q^{11}+71q^{25}+\cdots\)
2304.3.g.u	$2304$	$3$	2304.g	4.b	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}q^{5}-\zeta_{12}^{3}q^{7}-\zeta_{12}^{2}q^{11}+\cdots\)
2304.3.g.v	$2304$	$3$	2304.g	4.b	$2$	$4$	$4$	$62.779$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}+2\zeta_{12}^{3}q^{11}+\cdots\)
2304.3.g.w	$2304$	$3$	2304.g	4.b	$2$	$4$	$4$	$62.779$	\(\Q(\sqrt{-2}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+\beta _{1}q^{7}+\beta _{2}q^{11}+4q^{13}+\cdots\)
2304.3.g.x	$2304$	$3$	2304.g	4.b	$2$	$4$	$4$	$62.779$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(16\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(4+\beta _{2})q^{5}+\beta _{1}q^{7}+(-4\beta _{1}-\beta _{3})q^{11}+\cdots\)
2304.3.g.y	$2304$	$3$	2304.g	4.b	$2$	$8$	$8$	$62.779$	8.0.3317760000.5	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{5}+\beta _{5}q^{7}+\beta _{4}q^{11}+\beta _{1}q^{13}+\cdots\)
2304.3.g.z	$2304$	$3$	2304.g	4.b	$2$	$8$	$8$	$62.779$	8.0.22581504.2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{5}-\beta _{7}q^{7}+\beta _{6}q^{11}+(\beta _{1}-\beta _{4}+\cdots)q^{13}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(2304, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 14}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 15}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(576, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(768, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1152, [\chi])\)\(^{\oplus 2}\)