Space of modular forms of level 1540, weight 2, and Character 1540.h

• Label: 1540.2.h
• Level: $1540$
• Weight: $2$
• Character orbit: 1540.h
• Rep. character: $\chi_{1540}(461,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $576$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1540 = 2^{2} \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1540.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 77 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(576\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1540, [\chi])\).

	Total	New	Old
Modular forms	300	32	268
Cusp forms	276	32	244
Eisenstein series	24	0	24

Trace form

\( 32 q - 36 q^{9} - 6 q^{11} - 4 q^{15} + 24 q^{23} - 32 q^{25} - 16 q^{37} + 16 q^{49} + 8 q^{53} + 8 q^{67} - 80 q^{71} - 8 q^{77} + 96 q^{81} - 52 q^{91} + 8 q^{93} - 4 q^{99}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1540, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1540.2.h.a	$1540$	$2$	1540.h	77.b	$2$	$32$	$32$	$12.297$		None		✓	✓	✓	1540.2.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1540, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1540, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(770, [\chi])\)\(^{\oplus 2}\)