Space of modular forms of level 215, weight 2, and Character 215.u

• Label: 215.2.u
• Level: $215$
• Weight: $2$
• Character orbit: 215.u
• Rep. character: $\chi_{215}(9,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $240$
• Newform subspaces: $1$
• Sturm bound: $44$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 215 = 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	215.u (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 215 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(44\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(215, [\chi])\).

	Total	New	Old
Modular forms	288	288	0
Cusp forms	240	240	0
Eisenstein series	48	48	0

Trace form

\( 240 q + 16 q^{4} - 15 q^{5} - 14 q^{6} - 58 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(215, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
215.2.u.a	$215$	$2$	215.u	215.u	$42$	$240$	$20$	$1.717$		None		$4$	$0$	\(0\)	\(0\)	\(-15\)	\(0\)		$\mathrm{SU}(2)[C_{42}]$