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

• Label: 2352.3.m
• Level: $2352$
• Weight: $3$
• Character orbit: 2352.m
• Rep. character: $\chi_{2352}(1471,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $18$
• Sturm bound: $1344$
• Trace bound: $41$

Defining parameters

Level:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	2352.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1344\)
Trace bound:			\(41\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	944	82	862
Cusp forms	848	82	766
Eisenstein series	96	0	96

Trace form

\( 82 q + 12 q^{5} - 246 q^{9} + O(q^{10}) \)

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.m.a	$2352$	$3$	2352.m	4.b	$2$	$2$	$2$	$64.087$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{6}q^{3}-6q^{5}-3q^{9}+12\zeta_{6}q^{11}+\cdots\)
2352.3.m.b	$2352$	$3$	2352.m	4.b	$2$	$2$	$2$	$64.087$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{6}q^{3}-4q^{5}-3q^{9}-8\zeta_{6}q^{11}+\cdots\)
2352.3.m.c	$2352$	$3$	2352.m	4.b	$2$	$2$	$2$	$64.087$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{6}q^{3}+4q^{5}-3q^{9}-8\zeta_{6}q^{11}+\cdots\)
2352.3.m.d	$2352$	$3$	2352.m	4.b	$2$	$4$	$4$	$64.087$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(-24\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-6+\beta _{1})q^{5}-3q^{9}+(6\beta _{2}+\cdots)q^{11}+\cdots\)
2352.3.m.e	$2352$	$3$	2352.m	4.b	$2$	$4$	$4$	$64.087$	\(\Q(\sqrt{-3}, \sqrt{37})\)	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-3-\beta _{2})q^{5}-3q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
2352.3.m.f	$2352$	$3$	2352.m	4.b	$2$	$4$	$4$	$64.087$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-1+\beta _{1})q^{5}-3q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)
2352.3.m.g	$2352$	$3$	2352.m	4.b	$2$	$4$	$4$	$64.087$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}-3q^{9}+(7\beta _{1}+5\beta _{3})q^{11}+\cdots\)
2352.3.m.h	$2352$	$3$	2352.m	4.b	$2$	$4$	$4$	$64.087$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}-3q^{9}+(-7\beta _{1}-5\beta _{3})q^{11}+\cdots\)
2352.3.m.i	$2352$	$3$	2352.m	4.b	$2$	$4$	$4$	$64.087$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+2q^{5}-3q^{9}+(-4\beta _{1}+\beta _{3})q^{11}+\cdots\)
2352.3.m.j	$2352$	$3$	2352.m	4.b	$2$	$4$	$4$	$64.087$	\(\Q(\sqrt{-3}, \sqrt{37})\)	None		$2$	$0$	\(0\)	\(0\)	\(12\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(3+\beta _{2})q^{5}-3q^{9}+(\beta _{1}+\beta _{3})q^{11}+\cdots\)
2352.3.m.k	$2352$	$3$	2352.m	4.b	$2$	$4$	$4$	$64.087$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(5-\beta _{1})q^{5}-3q^{9}+(3\beta _{2}+\cdots)q^{11}+\cdots\)
2352.3.m.l	$2352$	$3$	2352.m	4.b	$2$	$4$	$4$	$64.087$	\(\Q(\sqrt{2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(0\)	\(24\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(6+\beta _{1})q^{5}-3q^{9}+(-6\beta _{2}+\cdots)q^{11}+\cdots\)
2352.3.m.m	$2352$	$3$	2352.m	4.b	$2$	$6$	$6$	$64.087$	6.0.2682209403.3	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-1+\beta _{3})q^{5}-3q^{9}+(\beta _{2}+\cdots)q^{11}+\cdots\)
2352.3.m.n	$2352$	$3$	2352.m	4.b	$2$	$6$	$6$	$64.087$	6.0.1364138928.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}-3q^{9}+\beta _{4}q^{11}+\cdots\)
2352.3.m.o	$2352$	$3$	2352.m	4.b	$2$	$6$	$6$	$64.087$	6.0.1364138928.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{3}q^{5}-3q^{9}+\beta _{4}q^{11}+\cdots\)
2352.3.m.p	$2352$	$3$	2352.m	4.b	$2$	$6$	$6$	$64.087$	6.0.2682209403.3	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(1-\beta _{3})q^{5}-3q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
2352.3.m.q	$2352$	$3$	2352.m	4.b	$2$	$8$	$8$	$64.087$	8.0.339738624.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{5}-3q^{9}+(-2\beta _{6}+\cdots)q^{11}+\cdots\)
2352.3.m.r	$2352$	$3$	2352.m	4.b	$2$	$8$	$8$	$64.087$	8.0.339738624.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}+(\beta _{1}-\beta _{4})q^{5}-3q^{9}+(\beta _{5}+\cdots)q^{11}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)