Space of modular forms of level 1520, weight 1, and Character 1520.m

• Label: 1520.1.m
• Level: $1520$
• Weight: $1$
• Character orbit: 1520.m
• Rep. character: $\chi_{1520}(1329,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1520.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(240\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1520, [\chi])\).

	Total	New	Old
Modular forms	38	7	31
Cusp forms	26	5	21
Eisenstein series	12	2	10

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	5	0	0	0

Trace form

\( 5 q - 2 q^{5} - q^{9} - q^{19} + 2 q^{25} + 3 q^{35} + 4 q^{39} - 2 q^{45} - q^{49} + 3 q^{55} + q^{81} + 3 q^{85} - 2 q^{95}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1520, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1520.1.m.a	$1520$	$1$	1520.m	95.d	$2$	$1$	$1$	$0.759$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \)	\(\Q(\sqrt{5}) \)	✓				95.1.d.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q+q^{5}-q^{9}+2q^{11}-q^{19}+q^{25}+\cdots\)
1520.1.m.b	$1520$	$1$	1520.m	95.d	$2$	$2$	$2$	$0.759$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-95}) \)	None	✓				95.1.d.b	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\beta q^{3}-q^{5}+q^{9}-\beta q^{13}+\beta q^{15}+\cdots\)
1520.1.m.c	$1520$	$1$	1520.m	95.d	$2$	$2$	$2$	$0.759$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-19}) \)	None					380.1.g.a	$4$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-\zeta_{6}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{9}-q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1520, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1520, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 3}\)