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

• Label: 480.2.b
• Level: $480$
• Weight: $2$
• Character orbit: 480.b
• Rep. character: $\chi_{480}(431,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	480.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(23\)

Dimensions

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

	Total	New	Old
Modular forms	112	16	96
Cusp forms	80	16	64
Eisenstein series	32	0	32

Trace form

\( 16 q + 8 q^{19} + 16 q^{25} + 24 q^{27} - 8 q^{33} - 32 q^{49} - 40 q^{51} - 8 q^{57} + 64 q^{67} - 16 q^{73} + 16 q^{81} - 48 q^{91} + 16 q^{97} - 32 q^{99}+O(q^{100}) \)

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.b.a	$480$	$2$	480.b	24.f	$2$	$8$	$8$	$3.833$	8.0.1649659456.5	None					120.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}-q^{5}-\beta _{2}q^{7}+(-\beta _{3}-\beta _{5}+\cdots)q^{9}+\cdots\)
480.2.b.b	$480$	$2$	480.b	24.f	$2$	$8$	$8$	$3.833$	8.0.1649659456.5	None					120.2.b.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+q^{5}+\beta _{2}q^{7}+(-\beta _{3}-\beta _{5}+\cdots)q^{9}+\cdots\)

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

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