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

• Label: 480.2.f
• Level: $480$
• Weight: $2$
• Character orbit: 480.f
• Rep. character: $\chi_{480}(289,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $5$
• Sturm bound: $192$
• Trace bound: $15$

Defining parameters

Level:	\( N \)	\(=\)	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	480.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(192\)
Trace bound:			\(15\)
Distinguishing \(T_p\):			\(7\), \(11\), \(19\)

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

\( 12 q - 4 q^{5} - 12 q^{9} - 20 q^{25} + 8 q^{29} + 40 q^{41} + 4 q^{45} - 12 q^{49} - 8 q^{61} + 12 q^{81} - 64 q^{85} - 40 q^{89}+O(q^{100}) \)

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.f.a	$480$	$2$	480.f	5.b	$2$	$2$	$2$	$3.833$	\(\Q(\sqrt{-1}) \)	None		✓			480.2.f.a	$2$	$1$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(i-2)q^{5}-2 i q^{7}-q^{9}+\cdots\)
480.2.f.b	$480$	$2$	480.f	5.b	$2$	$2$	$2$	$3.833$	\(\Q(\sqrt{-1}) \)	None		✓			480.2.f.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-i-2)q^{5}-2 i q^{7}-q^{9}+\cdots\)
480.2.f.c	$480$	$2$	480.f	5.b	$2$	$2$	$2$	$3.833$	\(\Q(\sqrt{-1}) \)	None		✓			480.2.f.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(2 i+1)q^{5}+4 i q^{7}-q^{9}+\cdots\)
480.2.f.d	$480$	$2$	480.f	5.b	$2$	$2$	$2$	$3.833$	\(\Q(\sqrt{-1}) \)	None		✓			480.2.f.c	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{3}+(-2 i+1)q^{5}+4 i q^{7}+\cdots\)
480.2.f.e	$480$	$2$	480.f	5.b	$2$	$4$	$4$	$3.833$	\(\Q(i, \sqrt{5})\)	None		✓	✓		480.2.f.e	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{2}q^{5}-2\beta _{1}q^{7}-q^{9}-2\beta _{3}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(480, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)