Space of modular forms of level 1900, weight 2, and Character 1900.s

• Label: 1900.2.s
• Level: $1900$
• Weight: $2$
• Character orbit: 1900.s
• Rep. character: $\chi_{1900}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $60$
• Newform subspaces: $5$
• Sturm bound: $600$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(600\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).

	Total	New	Old
Modular forms	636	60	576
Cusp forms	564	60	504
Eisenstein series	72	0	72

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1900.2.s.a	$1900$	$2$	1900.s	95.i	$6$	$4$	$2$	$15.172$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{9}-4q^{11}+(-\zeta_{12}+\cdots)q^{13}+\cdots\)
1900.2.s.b	$1900$	$2$	1900.s	95.i	$6$	$4$	$2$	$15.172$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}-2\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
1900.2.s.c	$1900$	$2$	1900.s	95.i	$6$	$12$	$6$	$15.172$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{6}+\beta _{11})q^{3}+(\beta _{10}+\beta _{11})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.s.d	$1900$	$2$	1900.s	95.i	$6$	$16$	$8$	$15.172$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{3}+\beta _{14}q^{7}+(\beta _{4}-\beta _{5}+\beta _{10}+\cdots)q^{9}+\cdots\)
1900.2.s.e	$1900$	$2$	1900.s	95.i	$6$	$24$	$12$	$15.172$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)