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

• Label: 1520.2.d
• Level: $1520$
• Weight: $2$
• Character orbit: 1520.d
• Rep. character: $\chi_{1520}(609,\cdot)$
• Character field: $\Q$
• Dimension: $54$
• Newform subspaces: $11$
• Sturm bound: $480$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(480\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	252	54	198
Cusp forms	228	54	174
Eisenstein series	24	0	24

Trace form

\( 54 q + 2 q^{5} - 54 q^{9} + O(q^{10}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1520.2.d.a	$1520$	$2$	1520.d	5.b	$2$	$2$	$2$	$12.137$	\(\Q(\sqrt{-1}) \)	None					760.2.d.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+(-1-i)q^{5}+iq^{7}-q^{9}+\cdots\)
1520.2.d.b	$1520$	$2$	1520.d	5.b	$2$	$2$	$2$	$12.137$	\(\Q(\sqrt{-1}) \)	None					95.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-i)q^{5}-iq^{7}+3q^{9}+4q^{11}+\cdots\)
1520.2.d.c	$1520$	$2$	1520.d	5.b	$2$	$4$	$4$	$12.137$	\(\Q(i, \sqrt{5})\)	None					760.2.d.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1520.2.d.d	$1520$	$2$	1520.d	5.b	$2$	$4$	$4$	$12.137$	\(\Q(\zeta_{8})\)	None					760.2.d.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
1520.2.d.e	$1520$	$2$	1520.d	5.b	$2$	$4$	$4$	$12.137$	\(\Q(\zeta_{8})\)	None					190.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
1520.2.d.f	$1520$	$2$	1520.d	5.b	$2$	$4$	$4$	$12.137$	\(\Q(\sqrt{-2}, \sqrt{5})\)	None					380.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
1520.2.d.g	$1520$	$2$	1520.d	5.b	$2$	$4$	$4$	$12.137$	\(\Q(\zeta_{8})\)	None					760.2.d.d	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{3}+(1-\zeta_{8})q^{5}+(-\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1520.2.d.h	$1520$	$2$	1520.d	5.b	$2$	$6$	$6$	$12.137$	6.0.16516096.1	None					95.2.b.b	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+\beta _{3}q^{5}+(\beta _{1}+\beta _{4})q^{7}+(-3+\cdots)q^{9}+\cdots\)
1520.2.d.i	$1520$	$2$	1520.d	5.b	$2$	$6$	$6$	$12.137$	6.0.14077504.2	None					380.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+\beta _{5}q^{5}+(-\beta _{3}-\beta _{4})q^{7}+\cdots\)
1520.2.d.j	$1520$	$2$	1520.d	5.b	$2$	$6$	$6$	$12.137$	6.0.5161984.1	None					190.2.b.b	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(-\beta _{4}+\beta _{5})q^{7}+\cdots\)
1520.2.d.k	$1520$	$2$	1520.d	5.b	$2$	$12$	$12$	$12.137$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None			✓		760.2.d.e	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{11}q^{3}-\beta _{6}q^{5}+(\beta _{5}+\beta _{11})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1520, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(760, [\chi])\)\(^{\oplus 2}\)