Space of modular forms of level 302, weight 2, and Character 302.h

• Label: 302.2.h
• Level: $302$
• Weight: $2$
• Character orbit: 302.h
• Rep. character: $\chi_{302}(9,\cdot)$
• Character field: $\Q(\zeta_{25})$
• Dimension: $280$
• Newform subspaces: $2$
• Sturm bound: $76$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 302 = 2 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	302.h (of order \(25\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 151 \)
Character field:			\(\Q(\zeta_{25})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(76\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(302, [\chi])\).

	Total	New	Old
Modular forms	800	280	520
Cusp forms	720	280	440
Eisenstein series	80	0	80

Trace form

\( 280 q - 70 q^{4} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(302, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
302.2.h.a	$302$	$2$	302.h	151.h	$25$	$140$	$7$	$2.411$		None		$2$	$0$	\(-35\)	\(0\)	\(-5\)	\(-5\)		$\mathrm{SU}(2)[C_{25}]$
302.2.h.b	$302$	$2$	302.h	151.h	$25$	$140$	$7$	$2.411$		None		$2$	$0$	\(35\)	\(0\)	\(5\)	\(5\)		$\mathrm{SU}(2)[C_{25}]$

Decomposition of \(S_{2}^{\mathrm{old}}(302, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(302, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(151, [\chi])\)\(^{\oplus 2}\)