Space of modular forms of level 950, weight 2, and Character 950.j

• Label: 950.2.j
• Level: $950$
• Weight: $2$
• Character orbit: 950.j
• Rep. character: $\chi_{950}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $60$
• Newform subspaces: $9$
• Sturm bound: $300$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(300\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(950, [\chi])\).

	Total	New	Old
Modular forms	324	60	264
Cusp forms	276	60	216
Eisenstein series	48	0	48

Trace form

\( 60 q + 30 q^{4} + 30 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(950, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
950.2.j.a	$950$	$2$	950.j	95.i	$6$	$4$	$2$	$7.586$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{6}+\cdots\)
950.2.j.b	$950$	$2$	950.j	95.i	$6$	$4$	$2$	$7.586$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{6}+\cdots\)
950.2.j.c	$950$	$2$	950.j	95.i	$6$	$4$	$2$	$7.586$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+4\zeta_{12}^{3}q^{7}+\cdots\)
950.2.j.d	$950$	$2$	950.j	95.i	$6$	$4$	$2$	$7.586$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
950.2.j.e	$950$	$2$	950.j	95.i	$6$	$4$	$2$	$7.586$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
950.2.j.f	$950$	$2$	950.j	95.i	$6$	$8$	$4$	$7.586$	8.0.1731891456.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
950.2.j.g	$950$	$2$	950.j	95.i	$6$	$8$	$4$	$7.586$	8.0.49787136.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{4}q^{2}-\beta _{1}q^{3}+(1+\beta _{3})q^{4}+\beta _{7}q^{6}+\cdots\)
950.2.j.h	$950$	$2$	950.j	95.i	$6$	$8$	$4$	$7.586$	8.0.49787136.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{7})q^{3}+(1-\beta _{5})q^{4}+\cdots\)
950.2.j.i	$950$	$2$	950.j	95.i	$6$	$16$	$8$	$7.586$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}-\beta _{4})q^{2}-\beta _{14}q^{3}+(1+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 2}\)