Space of modular forms of level 1320, weight 2, and Character 1320.d

• Label: 1320.2.d
• Level: $1320$
• Weight: $2$
• Character orbit: 1320.d
• Rep. character: $\chi_{1320}(529,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $4$
• Sturm bound: $576$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1320.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(576\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1320, [\chi])\).

	Total	New	Old
Modular forms	304	32	272
Cusp forms	272	32	240
Eisenstein series	32	0	32

Trace form

\( 32 q - 8 q^{5} - 32 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1320, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1320.2.d.a	$1320$	$2$	1320.d	5.b	$2$	$6$	$6$	$10.540$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(-\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
1320.2.d.b	$1320$	$2$	1320.d	5.b	$2$	$6$	$6$	$10.540$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+(\beta _{1}+\beta _{5})q^{5}+(\beta _{1}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
1320.2.d.c	$1320$	$2$	1320.d	5.b	$2$	$10$	$10$	$10.540$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{6}q^{5}-\beta _{1}q^{7}-q^{9}-q^{11}+\cdots\)
1320.2.d.d	$1320$	$2$	1320.d	5.b	$2$	$10$	$10$	$10.540$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}-\beta _{1}q^{5}-\beta _{9}q^{7}-q^{9}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)