Space of modular forms of level 1950, weight 2, and Character 1950.y

• Label: 1950.2.y
• Level: $1950$
• Weight: $2$
• Character orbit: 1950.y
• Rep. character: $\chi_{1950}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $14$
• Sturm bound: $840$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.y (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 14 \)
Sturm bound:			\(840\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1950, [\chi])\).

	Total	New	Old
Modular forms	888	88	800
Cusp forms	792	88	704
Eisenstein series	96	0	96

Trace form

\( 88 q - 44 q^{4} + 44 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1950, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1950.2.y.a	$1950$	$2$	1950.y	65.l	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}^{2})q^{2}+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1950.2.y.b	$1950$	$2$	1950.y	65.l	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}^{2})q^{2}+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1950.2.y.c	$1950$	$2$	1950.y	65.l	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{2}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1950.2.y.d	$1950$	$2$	1950.y	65.l	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1950.2.y.e	$1950$	$2$	1950.y	65.l	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None		$2$	$1$	\(2\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1950.2.y.f	$1950$	$2$	1950.y	65.l	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1950.2.y.g	$1950$	$2$	1950.y	65.l	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\zeta_{12}^{2})q^{2}-\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
1950.2.y.h	$1950$	$2$	1950.y	65.l	$6$	$4$	$2$	$15.571$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1950.2.y.i	$1950$	$2$	1950.y	65.l	$6$	$8$	$4$	$15.571$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{24}^{4})q^{2}-\zeta_{24}^{2}q^{3}-\zeta_{24}^{4}q^{4}+\cdots\)
1950.2.y.j	$1950$	$2$	1950.y	65.l	$6$	$8$	$4$	$15.571$	8.0.\(\cdots\).1	None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{6})q^{2}+(\beta _{2}+\beta _{5})q^{3}-\beta _{6}q^{4}+\cdots\)
1950.2.y.k	$1950$	$2$	1950.y	65.l	$6$	$8$	$4$	$15.571$	8.0.\(\cdots\).1	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{6})q^{2}+(-\beta _{2}-\beta _{5})q^{3}-\beta _{6}q^{4}+\cdots\)
1950.2.y.l	$1950$	$2$	1950.y	65.l	$6$	$8$	$4$	$15.571$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(4\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{24}^{4}q^{2}+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1950.2.y.m	$1950$	$2$	1950.y	65.l	$6$	$12$	$6$	$15.571$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\beta _{4})q^{2}-\beta _{9}q^{3}-\beta _{4}q^{4}+\beta _{8}q^{6}+\cdots\)
1950.2.y.n	$1950$	$2$	1950.y	65.l	$6$	$12$	$6$	$15.571$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{4})q^{2}+\beta _{9}q^{3}-\beta _{4}q^{4}+\beta _{8}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)