Space of modular forms of level 215, weight 6, and trivial character

• Label: 215.6.a
• Level: $215$
• Weight: $6$
• Character orbit: 215.a
• Rep. character: $\chi_{215}(1,\cdot)$
• Character field: $\Q$
• Dimension: $70$
• Newform subspaces: $4$
• Sturm bound: $132$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 215 = 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	215.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(132\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(215))\).

	Total	New	Old
Modular forms	112	70	42
Cusp forms	108	70	38
Eisenstein series	4	0	4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)	\(43\)	Fricke	Dim
\(+\)	\(+\)	$+$	\(15\)
\(+\)	\(-\)	$-$	\(20\)
\(-\)	\(+\)	$-$	\(22\)
\(-\)	\(-\)	$+$	\(13\)
Plus space		\(+\)	\(28\)
Minus space		\(-\)	\(42\)

Trace form

\( 70 q + 1100 q^{4} - 48 q^{6} + 852 q^{8} + 5450 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(215))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		5	43
215.6.a.a	$215$	$6$	215.a	1.a	$1$	$13$	$13$	$34.483$	\(\mathbb{Q}[x]/(x^{13} - \cdots)\)	None	✓	$1$	$1$	\(-7\)	\(-16\)	\(325\)	\(-372\)		$-$	$-$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1-\beta _{3})q^{3}+(9+\cdots)q^{4}+\cdots\)
215.6.a.b	$215$	$6$	215.a	1.a	$1$	$15$	$15$	$34.483$	\(\mathbb{Q}[x]/(x^{15} - \cdots)\)	None	✓	$1$	$1$	\(-5\)	\(-20\)	\(-375\)	\(-118\)		$+$	$+$	$+$	$2^{5}$	$\mathrm{SU}(2)$	\(q-\beta _{1}q^{2}+(-1+\beta _{6})q^{3}+(14+\beta _{2}+\cdots)q^{4}+\cdots\)
215.6.a.c	$215$	$6$	215.a	1.a	$1$	$20$	$20$	$34.483$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None	✓	$1$	$0$	\(7\)	\(16\)	\(-500\)	\(372\)		$+$	$-$	$-$	$2^{5}$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{4})q^{3}+(17+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
215.6.a.d	$215$	$6$	215.a	1.a	$1$	$22$	$22$	$34.483$		None	✓	$1$	$0$	\(5\)	\(20\)	\(550\)	\(118\)		$-$	$+$	$-$		$\mathrm{SU}(2)$

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(215))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(215)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 2}\)