Space of modular forms of level 3120, weight 2, and Character 3120.k

• Label: 3120.2.k
• Level: $3120$
• Weight: $2$
• Character orbit: 3120.k
• Rep. character: $\chi_{3120}(911,\cdot)$
• Character field: $\Q$
• Dimension: $96$
• Newform subspaces: $9$
• Sturm bound: $1344$
• Trace bound: $33$

Defining parameters

Level:	\( N \)	\(=\)	\( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3120.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1344\)
Trace bound:			\(33\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3120, [\chi])\).

	Total	New	Old
Modular forms	696	96	600
Cusp forms	648	96	552
Eisenstein series	48	0	48

Trace form

\( 96 q - 24 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3120, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3120.2.k.a	$3120$	$2$	3120.k	12.b	$2$	$4$	$4$	$24.913$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-3q^{9}-2\zeta_{12}^{3}q^{11}+\cdots\)
3120.2.k.b	$3120$	$2$	3120.k	12.b	$2$	$4$	$4$	$24.913$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-2\zeta_{12}^{2}q^{7}+\cdots\)
3120.2.k.c	$3120$	$2$	3120.k	12.b	$2$	$4$	$4$	$24.913$	\(\Q(i, \sqrt{6})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
3120.2.k.d	$3120$	$2$	3120.k	12.b	$2$	$4$	$4$	$24.913$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{3}q^{3}+\zeta_{12}q^{5}-\zeta_{12}^{2}q^{7}+3q^{9}+\cdots\)
3120.2.k.e	$3120$	$2$	3120.k	12.b	$2$	$4$	$4$	$24.913$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{3}q^{3}+\zeta_{12}q^{5}-\zeta_{12}^{2}q^{7}+3q^{9}+\cdots\)
3120.2.k.f	$3120$	$2$	3120.k	12.b	$2$	$8$	$8$	$24.913$	\(\Q(\zeta_{16})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{16}^{3}-\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}+\zeta_{16}^{4}q^{5}+\cdots\)
3120.2.k.g	$3120$	$2$	3120.k	12.b	$2$	$16$	$16$	$24.913$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}+\beta _{4}q^{5}+(\beta _{1}+\beta _{6}+\beta _{7}-\beta _{9}+\cdots)q^{7}+\cdots\)
3120.2.k.h	$3120$	$2$	3120.k	12.b	$2$	$20$	$20$	$24.913$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{3}+\beta _{1}q^{5}+\beta _{9}q^{7}+(-\beta _{8}-\beta _{19})q^{9}+\cdots\)
3120.2.k.i	$3120$	$2$	3120.k	12.b	$2$	$32$	$32$	$24.913$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3120, [\chi]) \cong \)