Space of modular forms of level 1900, weight 4, and Character 1900.c

• Label: 1900.4.c
• Level: $1900$
• Weight: $4$
• Character orbit: 1900.c
• Rep. character: $\chi_{1900}(1749,\cdot)$
• Character field: $\Q$
• Dimension: $82$
• Newform subspaces: $9$
• Sturm bound: $1200$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1900.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1200\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1900, [\chi])\).

	Total	New	Old
Modular forms	918	82	836
Cusp forms	882	82	800
Eisenstein series	36	0	36

Trace form

\( 82 q - 958 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1900, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1900.4.c.a	$1900$	$4$	1900.c	5.b	$2$	$2$	$2$	$112.104$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-19iq^{7}+26q^{9}+20q^{11}+\cdots\)
1900.4.c.b	$1900$	$4$	1900.c	5.b	$2$	$4$	$4$	$112.104$	\(\Q(i, \sqrt{33})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-5\beta _{1}-\beta _{2})q^{7}+(12+\beta _{3})q^{9}+\cdots\)
1900.4.c.c	$1900$	$4$	1900.c	5.b	$2$	$6$	$6$	$112.104$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+(-\beta _{2}-6\beta _{4}+\cdots)q^{7}+\cdots\)
1900.4.c.d	$1900$	$4$	1900.c	5.b	$2$	$8$	$8$	$112.104$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+(-\beta _{2}-\beta _{3}+\beta _{4})q^{7}+(-26+\cdots)q^{9}+\cdots\)
1900.4.c.e	$1900$	$4$	1900.c	5.b	$2$	$8$	$8$	$112.104$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}-\beta _{3}-\beta _{4})q^{7}+\cdots\)
1900.4.c.f	$1900$	$4$	1900.c	5.b	$2$	$8$	$8$	$112.104$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{2}-\beta _{5})q^{3}+(\beta _{1}+4\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
1900.4.c.g	$1900$	$4$	1900.c	5.b	$2$	$10$	$10$	$112.104$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(\beta _{1}+\beta _{2}+\beta _{9})q^{7}+(-8+\cdots)q^{9}+\cdots\)
1900.4.c.h	$1900$	$4$	1900.c	5.b	$2$	$18$	$18$	$112.104$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 3^{2}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}+(\beta _{9}+\beta _{14})q^{7}+(-15+\beta _{4}+\cdots)q^{9}+\cdots\)
1900.4.c.i	$1900$	$4$	1900.c	5.b	$2$	$18$	$18$	$112.104$	\(\mathbb{Q}[x]/(x^{18} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}-\beta _{11}q^{7}+(-10-\beta _{1})q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)