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

• Label: 480.2.k
• Level: $480$
• Weight: $2$
• Character orbit: 480.k
• Rep. character: $\chi_{480}(241,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	480.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	112	8	104
Cusp forms	80	8	72
Eisenstein series	32	0	32

Trace form

\( 8 q - 8 q^{7} - 8 q^{9} + 4 q^{15} + 16 q^{23} - 8 q^{25} - 8 q^{31} + 24 q^{49} - 16 q^{55} - 16 q^{57} + 8 q^{63} + 16 q^{71} - 16 q^{73} - 8 q^{79} + 8 q^{81} - 24 q^{87} + 16 q^{97}+O(q^{100}) \)

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.k.a	$480$	$2$	480.k	8.b	$2$	$2$	$2$	$3.833$	\(\Q(\sqrt{-1}) \)	None					120.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+i q^{5}-2 q^{7}-q^{9}+4 i q^{11}+\cdots\)
480.2.k.b	$480$	$2$	480.k	8.b	$2$	$6$	$6$	$3.833$	6.0.399424.1	None			✓		120.2.k.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+\beta _{2}q^{5}+(-1+\beta _{3})q^{7}-q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(480, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)