Space of modular forms of level 1520, weight 2, and Character 1520.g

• Label: 1520.2.g
• Level: $1520$
• Weight: $2$
• Character orbit: 1520.g
• Rep. character: $\chi_{1520}(1519,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $7$
• Sturm bound: $480$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 380 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(480\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(7\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1520, [\chi])\).

	Total	New	Old
Modular forms	252	60	192
Cusp forms	228	60	168
Eisenstein series	24	0	24

Trace form

\( 60 q - 60 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1520, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1520.2.g.a	$1520$	$2$	1520.g	380.d	$2$	$2$	$2$	$12.137$	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(-1\)	\(-6\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta q^{5}-3q^{7}+3q^{9}+(1-2\beta )q^{11}+\cdots\)
1520.2.g.b	$1520$	$2$	1520.g	380.d	$2$	$2$	$2$	$12.137$	\(\Q(\sqrt{-19}) \)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(-1\)	\(6\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1+\beta )q^{5}+3q^{7}+3q^{9}+(1-2\beta )q^{11}+\cdots\)
1520.2.g.c	$1520$	$2$	1520.g	380.d	$2$	$4$	$4$	$12.137$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(1\)	\(-6\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{3}q^{5}+(-2-\beta _{1}-\beta _{3})q^{7}+3q^{9}+\cdots\)
1520.2.g.d	$1520$	$2$	1520.g	380.d	$2$	$4$	$4$	$12.137$	\(\Q(\sqrt{-3}, \sqrt{-19})\)	\(\Q(\sqrt{-19}) \)		$4$	$0$	\(0\)	\(0\)	\(1\)	\(6\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{5}+(2+\beta _{1}+\beta _{3})q^{7}+3q^{9}+\cdots\)
1520.2.g.e	$1520$	$2$	1520.g	380.d	$2$	$16$	$16$	$12.137$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}-\beta _{14}q^{5}-\beta _{10}q^{7}+(-2+\cdots)q^{9}+\cdots\)
1520.2.g.f	$1520$	$2$	1520.g	380.d	$2$	$16$	$16$	$12.137$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+\beta _{8}q^{7}+\cdots\)
1520.2.g.g	$1520$	$2$	1520.g	380.d	$2$	$16$	$16$	$12.137$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+\beta _{15}q^{5}+\beta _{10}q^{7}+(-2+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1520, [\chi]) \cong \)