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

• Label: 480.2.h
• Level: $480$
• Weight: $2$
• Character orbit: 480.h
• Rep. character: $\chi_{480}(191,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $192$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	480.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(192\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(7\), \(11\), \(23\)

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

\( 16 q - 8 q^{9} + O(q^{10}) \)

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.h.a	$480$	$2$	480.h	12.b	$2$	$4$	$4$	$3.833$	\(\Q(\zeta_{8})\)	None		✓			480.2.h.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}-1)q^{3}+\beta_1 q^{5}+(2\beta_{2}-2\beta_1)q^{7}+\cdots\)
480.2.h.b	$480$	$2$	480.h	12.b	$2$	$4$	$4$	$3.833$	\(\Q(\zeta_{8})\)	None		✓			480.2.h.b	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+\cdots\)
480.2.h.c	$480$	$2$	480.h	12.b	$2$	$4$	$4$	$3.833$	\(\Q(\zeta_{8})\)	None		✓			480.2.h.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+1)q^{3}+\beta_1 q^{5}+(-2\beta_{2}+2\beta_1)q^{7}+\cdots\)
480.2.h.d	$480$	$2$	480.h	12.b	$2$	$4$	$4$	$3.833$	\(\Q(\zeta_{8})\)	None		✓			480.2.h.b	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(480, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)