Space of modular forms of level 2352, weight 2, and Character 2352.h

• Label: 2352.2.h
• Level: $2352$
• Weight: $2$
• Character orbit: 2352.h
• Rep. character: $\chi_{2352}(2255,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $16$
• Sturm bound: $896$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2352.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 16 \)
Sturm bound:			\(896\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

	Total	New	Old
Modular forms	496	82	414
Cusp forms	400	82	318
Eisenstein series	96	0	96

Trace form

\( 82 q - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2352.2.h.a	$2352$	$2$	2352.h	12.b	$2$	$2$	$2$	$18.781$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{6}q^{3}-3q^{9}-7q^{13}+3\zeta_{6}q^{19}+\cdots\)
2352.2.h.b	$2352$	$2$	2352.h	12.b	$2$	$2$	$2$	$18.781$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{6}q^{3}-3q^{9}-5q^{13}+5\zeta_{6}q^{19}+\cdots\)
2352.2.h.c	$2352$	$2$	2352.h	12.b	$2$	$2$	$2$	$18.781$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{6}q^{3}-3q^{9}+2q^{13}+2\zeta_{6}q^{19}+\cdots\)
2352.2.h.d	$2352$	$2$	2352.h	12.b	$2$	$2$	$2$	$18.781$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\zeta_{6}q^{3}-3q^{9}+5q^{13}-5\zeta_{6}q^{19}+\cdots\)
2352.2.h.e	$2352$	$2$	2352.h	12.b	$2$	$2$	$2$	$18.781$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\zeta_{6}q^{3}-3q^{9}+7q^{13}-3\zeta_{6}q^{19}+\cdots\)
2352.2.h.f	$2352$	$2$	2352.h	12.b	$2$	$4$	$4$	$18.781$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-1-2\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
2352.2.h.g	$2352$	$2$	2352.h	12.b	$2$	$4$	$4$	$18.781$	\(\Q(\sqrt{-3}, \sqrt{-14})\)	\(\Q(\sqrt{-21}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}-3q^{9}-\beta _{3}q^{11}+\cdots\)
2352.2.h.h	$2352$	$2$	2352.h	12.b	$2$	$4$	$4$	$18.781$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+(1-2\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
2352.2.h.i	$2352$	$2$	2352.h	12.b	$2$	$4$	$4$	$18.781$	\(\Q(i, \sqrt{11})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}+\beta _{2})q^{3}+(-1-2\beta _{3})q^{5}+\cdots\)
2352.2.h.j	$2352$	$2$	2352.h	12.b	$2$	$4$	$4$	$18.781$	\(\Q(i, \sqrt{11})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-1-2\beta _{3})q^{5}+(3+\beta _{3})q^{9}+\cdots\)
2352.2.h.k	$2352$	$2$	2352.h	12.b	$2$	$4$	$4$	$18.781$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-1-2\zeta_{8}^{2}+\cdots)q^{9}+\cdots\)
2352.2.h.l	$2352$	$2$	2352.h	12.b	$2$	$8$	$8$	$18.781$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{24}^{2}q^{3}+\zeta_{24}^{4}q^{5}-\zeta_{24}^{5}q^{9}+\cdots\)
2352.2.h.m	$2352$	$2$	2352.h	12.b	$2$	$8$	$8$	$18.781$	8.0.8275904784.2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}-\beta _{7}q^{5}+(-\beta _{4}-\beta _{7})q^{9}+\cdots\)
2352.2.h.n	$2352$	$2$	2352.h	12.b	$2$	$8$	$8$	$18.781$	8.0.8275904784.2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{3}-\beta _{7}q^{5}+(-\beta _{2}+\beta _{7})q^{9}+\cdots\)
2352.2.h.o	$2352$	$2$	2352.h	12.b	$2$	$8$	$8$	$18.781$	8.0.56070144.2	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(1-\beta _{5}+\beta _{7})q^{9}+\cdots\)
2352.2.h.p	$2352$	$2$	2352.h	12.b	$2$	$16$	$16$	$18.781$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{3}+\beta _{13}q^{5}-\beta _{3}q^{9}-\beta _{7}q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \)