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

• Label: 950.2.e
• Level: $950$
• Weight: $2$
• Character orbit: 950.e
• Rep. character: $\chi_{950}(201,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $66$
• Newform subspaces: $15$
• Sturm bound: $300$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 15 \)
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	66	258
Cusp forms	276	66	210
Eisenstein series	48	0	48

Trace form

\( 66 q - q^{2} - q^{3} - 33 q^{4} + q^{6} - 12 q^{7} + 2 q^{8} - 36 q^{9} + O(q^{10}) \)

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.e.a	$950$	$2$	950.e	19.c	$3$	$2$	$1$	$7.586$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.b	$950$	$2$	950.e	19.c	$3$	$2$	$1$	$7.586$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.c	$950$	$2$	950.e	19.c	$3$	$2$	$1$	$7.586$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+4q^{7}+q^{8}+\cdots\)
950.2.e.d	$950$	$2$	950.e	19.c	$3$	$2$	$1$	$7.586$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(1\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.e	$950$	$2$	950.e	19.c	$3$	$2$	$1$	$7.586$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-4q^{7}-q^{8}+\cdots\)
950.2.e.f	$950$	$2$	950.e	19.c	$3$	$2$	$1$	$7.586$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{7}-q^{8}+3\zeta_{6}q^{9}+\cdots\)
950.2.e.g	$950$	$2$	950.e	19.c	$3$	$2$	$1$	$7.586$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(1\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
950.2.e.h	$950$	$2$	950.e	19.c	$3$	$4$	$2$	$7.586$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		$2$	$0$	\(-2\)	\(-1\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.i	$950$	$2$	950.e	19.c	$3$	$4$	$2$	$7.586$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(-2\)	\(1\)	\(0\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\beta _{1})q^{2}+\beta _{3}q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
950.2.e.j	$950$	$2$	950.e	19.c	$3$	$4$	$2$	$7.586$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(2\)	\(-1\)	\(0\)	\(4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{1})q^{2}-\beta _{3}q^{3}+\beta _{1}q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
950.2.e.k	$950$	$2$	950.e	19.c	$3$	$4$	$2$	$7.586$	\(\Q(\sqrt{-3}, \sqrt{7})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.l	$950$	$2$	950.e	19.c	$3$	$8$	$4$	$7.586$	8.0.\(\cdots\).1	None		$2$	$0$	\(-4\)	\(1\)	\(0\)	\(12\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{2}+\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.m	$950$	$2$	950.e	19.c	$3$	$8$	$4$	$7.586$	8.0.\(\cdots\).1	None		$2$	$0$	\(4\)	\(-1\)	\(0\)	\(-12\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.n	$950$	$2$	950.e	19.c	$3$	$10$	$5$	$7.586$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(-5\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{2}+\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
950.2.e.o	$950$	$2$	950.e	19.c	$3$	$10$	$5$	$7.586$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(5\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1-\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)