Space of modular forms of level 1170, weight 2, and Character 1170.cu

• Label: 1170.2.cu
• Level: $1170$
• Weight: $2$
• Character orbit: 1170.cu
• Rep. character: $\chi_{1170}(71,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $64$
• Newform subspaces: $6$
• Sturm bound: $504$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.cu (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(504\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1170, [\chi])\).

	Total	New	Old
Modular forms	1072	64	1008
Cusp forms	944	64	880
Eisenstein series	128	0	128

Trace form

\( 64 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1170, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1170.2.cu.a	$1170$	$2$	1170.cu	39.k	$12$	$8$	$2$	$9.342$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}-\zeta_{24}^{3}q^{5}+\cdots\)
1170.2.cu.b	$1170$	$2$	1170.cu	39.k	$12$	$8$	$2$	$9.342$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{5}+\cdots\)
1170.2.cu.c	$1170$	$2$	1170.cu	39.k	$12$	$8$	$2$	$9.342$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{5}+\cdots\)
1170.2.cu.d	$1170$	$2$	1170.cu	39.k	$12$	$8$	$2$	$9.342$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
1170.2.cu.e	$1170$	$2$	1170.cu	39.k	$12$	$16$	$4$	$9.342$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{3}q^{2}+(\beta _{6}-\beta _{11})q^{4}+(-\beta _{3}+\beta _{15})q^{5}+\cdots\)
1170.2.cu.f	$1170$	$2$	1170.cu	39.k	$12$	$16$	$4$	$9.342$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{14}q^{2}+\beta _{5}q^{4}-\beta _{13}q^{5}+(1-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1170, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)