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 - 10 * q^11 + 2 * q^19 + 8 * q^21 + 20 * q^29 + 12 * q^31 - 44 * q^39 - 20 * q^49 - 32 * q^51 + 12 * q^59 - 30 * q^61 - 40 * q^69 + 20 * q^71 + 48 * q^79 + 42 * q^81 - 44 * q^89 - 36 * q^91 + 38 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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					380.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}-\beta q^{7}-q^{9}+3\beta q^{13}-\beta q^{17}+\cdots\)
1900.2.c.b	$1900$	$2$	1900.c	5.b	$2$	$2$	$2$	$15.172$	\(\Q(\sqrt{-1}) \)	None					76.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{3}+3 i q^{7}-q^{9}+5 q^{11}+\cdots\)
1900.2.c.c	$1900$	$2$	1900.c	5.b	$2$	$2$	$2$	$15.172$	\(\Q(\sqrt{-1}) \)	None					380.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{7}+3 q^{9}-4 q^{11}+2\beta q^{13}+\cdots\)
1900.2.c.d	$1900$	$2$	1900.c	5.b	$2$	$4$	$4$	$15.172$	\(\Q(\zeta_{8})\)	None					380.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{3}+(-2\beta_{2}-\beta_1)q^{7}+\cdots\)
1900.2.c.e	$1900$	$2$	1900.c	5.b	$2$	$4$	$4$	$15.172$	\(\Q(\zeta_{12})\)	None					380.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{3}+(\beta_{2}-\beta_1)q^{7}+(\beta_{3}-1)q^{9}+\cdots\)
1900.2.c.f	$1900$	$2$	1900.c	5.b	$2$	$6$	$6$	$15.172$	6.0.6594624.1	None		✓			1900.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}-\beta _{4}-\beta _{5})q^{7}+\cdots\)
1900.2.c.g	$1900$	$2$	1900.c	5.b	$2$	$6$	$6$	$15.172$	6.0.4227136.2	None		✓			1900.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{1}q^{7}+\beta _{5}q^{9}-\beta _{2}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1900, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)