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

• Label: 950.2.u
• Level: $950$
• Weight: $2$
• Character orbit: 950.u
• Rep. character: $\chi_{950}(99,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $180$
• Newform subspaces: $8$
• Sturm bound: $300$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(300\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	972	180	792
Cusp forms	828	180	648
Eisenstein series	144	0	144

Trace form

\( 180 q + O(q^{10}) \)

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.u.a	$950$	$2$	950.u	95.p	$18$	$12$	$2$	$7.586$	\(\Q(\zeta_{36})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(\zeta_{36}-\zeta_{36}^{7})q^{2}+(-\zeta_{36}^{5}-\zeta_{36}^{9}+\cdots)q^{3}+\cdots\)
950.2.u.b	$950$	$2$	950.u	95.p	$18$	$12$	$2$	$7.586$	\(\Q(\zeta_{36})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+\zeta_{36}^{11}q^{2}+(\zeta_{36}+\zeta_{36}^{3}-\zeta_{36}^{9}+\cdots)q^{3}+\cdots\)
950.2.u.c	$950$	$2$	950.u	95.p	$18$	$12$	$2$	$7.586$	\(\Q(\zeta_{36})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q-\zeta_{36}^{11}q^{2}+(\zeta_{36}+\zeta_{36}^{3}-\zeta_{36}^{9}+\cdots)q^{3}+\cdots\)
950.2.u.d	$950$	$2$	950.u	95.p	$18$	$12$	$2$	$7.586$	\(\Q(\zeta_{36})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q-\zeta_{36}^{5}q^{2}+(-\zeta_{36}+\zeta_{36}^{3}+\zeta_{36}^{11})q^{3}+\cdots\)
950.2.u.e	$950$	$2$	950.u	95.p	$18$	$24$	$4$	$7.586$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
950.2.u.f	$950$	$2$	950.u	95.p	$18$	$24$	$4$	$7.586$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
950.2.u.g	$950$	$2$	950.u	95.p	$18$	$36$	$6$	$7.586$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
950.2.u.h	$950$	$2$	950.u	95.p	$18$	$48$	$8$	$7.586$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

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

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