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

• Label: 215.2.l
• Level: $215$
• Weight: $2$
• Character orbit: 215.l
• Rep. character: $\chi_{215}(7,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $80$
• Newform subspaces: $3$
• Sturm bound: $44$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 215 = 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	215.l (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 215 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(44\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

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

Trace form

\( 80 q - 6 q^{3} - 6 q^{5} - 8 q^{6} - 12 q^{7} + O(q^{10}) \)

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.l.a	$215$	$2$	215.l	215.l	$12$	$4$	$1$	$1.717$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-2\)	\(2\)	\(2\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)
215.2.l.b	$215$	$2$	215.l	215.l	$12$	$4$	$1$	$1.717$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(4\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}-\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1+\cdots)q^{3}+\cdots\)
215.2.l.c	$215$	$2$	215.l	215.l	$12$	$72$	$18$	$1.717$		None		$4$	$0$	\(0\)	\(-12\)	\(-6\)	\(-12\)		$\mathrm{SU}(2)[C_{12}]$