Space of modular forms of level 2352, weight 3, and Character 2352.f

• Label: 2352.3.f
• Level: $2352$
• Weight: $3$
• Character orbit: 2352.f
• Rep. character: $\chi_{2352}(97,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $13$
• Sturm bound: $1344$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2352.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 13 \)
Sturm bound:			\(1344\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2352, [\chi])\).

	Total	New	Old
Modular forms	944	80	864
Cusp forms	848	80	768
Eisenstein series	96	0	96

Trace form

\( 80 q - 240 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2352, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2352.3.f.a	$2352$	$3$	2352.f	7.b	$2$	$2$	$2$	$64.087$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{6}q^{3}-3\zeta_{6}q^{5}-3q^{9}-15q^{11}+\cdots\)
2352.3.f.b	$2352$	$3$	2352.f	7.b	$2$	$2$	$2$	$64.087$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}-2\zeta_{6}q^{5}-3q^{9}-10q^{11}+\cdots\)
2352.3.f.c	$2352$	$3$	2352.f	7.b	$2$	$2$	$2$	$64.087$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}-\zeta_{6}q^{5}-3q^{9}+3q^{11}-4\zeta_{6}q^{13}+\cdots\)
2352.3.f.d	$2352$	$3$	2352.f	7.b	$2$	$2$	$2$	$64.087$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{6}q^{3}-3\zeta_{6}q^{5}-3q^{9}+11q^{11}+\cdots\)
2352.3.f.e	$2352$	$3$	2352.f	7.b	$2$	$4$	$4$	$64.087$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{1}+2\beta _{2})q^{5}-3q^{9}+\cdots\)
2352.3.f.f	$2352$	$3$	2352.f	7.b	$2$	$4$	$4$	$64.087$	\(\Q(\sqrt{-3}, \sqrt{65})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2})q^{5}-3q^{9}+(8+\cdots)q^{11}+\cdots\)
2352.3.f.g	$2352$	$3$	2352.f	7.b	$2$	$8$	$8$	$64.087$	8.0.\(\cdots\).9	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{7})q^{5}-3q^{9}+(-5+\cdots)q^{11}+\cdots\)
2352.3.f.h	$2352$	$3$	2352.f	7.b	$2$	$8$	$8$	$64.087$	8.0.339738624.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(2\beta _{2}-\beta _{5}-\beta _{7})q^{5}-3q^{9}+\cdots\)
2352.3.f.i	$2352$	$3$	2352.f	7.b	$2$	$8$	$8$	$64.087$	8.0.339738624.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-\beta _{4}-2\beta _{5})q^{5}-3q^{9}+\cdots\)
2352.3.f.j	$2352$	$3$	2352.f	7.b	$2$	$8$	$8$	$64.087$	8.0.339738624.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(\beta _{4}+\beta _{5})q^{5}-3q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
2352.3.f.k	$2352$	$3$	2352.f	7.b	$2$	$8$	$8$	$64.087$	8.0.\(\cdots\).2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{2}-\beta _{5})q^{5}-3q^{9}+(3+\cdots)q^{11}+\cdots\)
2352.3.f.l	$2352$	$3$	2352.f	7.b	$2$	$8$	$8$	$64.087$	8.0.339738624.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(-\beta _{6}+\beta _{7})q^{5}-3q^{9}+(8+\cdots)q^{11}+\cdots\)
2352.3.f.m	$2352$	$3$	2352.f	7.b	$2$	$16$	$16$	$64.087$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-\beta _{2}+\beta _{11})q^{5}-3q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 20}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)