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

• Label: 1900.2.c
• Level: $1900$
• Weight: $2$
• Character orbit: 1900.c
• Rep. character: $\chi_{1900}(1749,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $7$
• Sturm bound: $600$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(600\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	318	26	292
Cusp forms	282	26	256
Eisenstein series	36	0	36

Trace form

\( 26 q - 26 q^{9} + O(q^{10}) \)

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.c.a	$1900$	$2$	1900.c	5.b	$2$	$2$	$2$	$15.172$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{7}-q^{9}+3iq^{13}-iq^{17}+\cdots\)
1900.2.c.b	$1900$	$2$	1900.c	5.b	$2$	$2$	$2$	$15.172$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+3iq^{7}-q^{9}+5q^{11}-4iq^{13}+\cdots\)
1900.2.c.c	$1900$	$2$	1900.c	5.b	$2$	$2$	$2$	$15.172$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{7}+3q^{9}-4q^{11}+2iq^{13}+3iq^{17}+\cdots\)
1900.2.c.d	$1900$	$2$	1900.c	5.b	$2$	$4$	$4$	$15.172$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}-\zeta_{8}^{2})q^{3}+(-\zeta_{8}-2\zeta_{8}^{2})q^{7}+\cdots\)
1900.2.c.e	$1900$	$2$	1900.c	5.b	$2$	$4$	$4$	$15.172$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{2}q^{3}+(-\zeta_{12}+\zeta_{12}^{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1900.2.c.f	$1900$	$2$	1900.c	5.b	$2$	$6$	$6$	$15.172$	6.0.6594624.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}-\beta _{4}-\beta _{5})q^{7}+\cdots\)
1900.2.c.g	$1900$	$2$	1900.c	5.b	$2$	$6$	$6$	$15.172$	6.0.4227136.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{1}q^{7}+\beta _{5}q^{9}-\beta _{2}q^{11}+\cdots\)

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

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