Space of modular forms of level 480, weight 2, and Character 480.d

• Label: 480.2.d
• Level: $480$
• Weight: $2$
• Character orbit: 480.d
• Rep. character: $\chi_{480}(49,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	480.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(480, [\chi])\).

	Total	New	Old
Modular forms	112	12	100
Cusp forms	80	12	68
Eisenstein series	32	0	32

Trace form

\( 12 q + 12 q^{9} + 4 q^{25} + 32 q^{31} + 16 q^{39} - 8 q^{41} - 12 q^{49} + 16 q^{55} - 24 q^{65} - 32 q^{71} - 32 q^{79} + 12 q^{81} - 40 q^{89} - 64 q^{95}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(480, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
480.2.d.a	$480$	$2$	480.d	40.f	$2$	$6$	$6$	$3.833$	6.0.839056.1	None					120.2.d.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots\)
480.2.d.b	$480$	$2$	480.d	40.f	$2$	$6$	$6$	$3.833$	6.0.839056.1	None					120.2.d.a	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}+(\beta _{1}+\beta _{5})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(480, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(480, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)