Space of modular forms of level 1900, weight 3, and Character 1900.e

• Label: 1900.3.e
• Level: $1900$
• Weight: $3$
• Character orbit: 1900.e
• Rep. character: $\chi_{1900}(1101,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $8$
• Sturm bound: $900$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1900.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(900\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1900, [\chi])\).

	Total	New	Old
Modular forms	618	64	554
Cusp forms	582	64	518
Eisenstein series	36	0	36

Trace form

\( 64 q + 9 q^{7} - 202 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1900, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1900.3.e.a	$1900$	$3$	1900.e	19.b	$2$	$2$	$2$	$51.771$	\(\Q(\sqrt{57}) \)	\(\Q(\sqrt{-19}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+(-1-3\beta )q^{7}+9q^{9}+(1-5\beta )q^{11}+\cdots\)
1900.3.e.b	$1900$	$3$	1900.e	19.b	$2$	$2$	$2$	$51.771$	\(\Q(\sqrt{-29}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{3}+q^{7}-20q^{9}+14q^{11}+3\beta q^{13}+\cdots\)
1900.3.e.c	$1900$	$3$	1900.e	19.b	$2$	$4$	$4$	$51.771$	\(\Q(\sqrt{6}, \sqrt{-14})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{2}q^{7}-5q^{9}+4q^{11}-3\beta _{1}q^{13}+\cdots\)
1900.3.e.d	$1900$	$3$	1900.e	19.b	$2$	$4$	$4$	$51.771$	\(\Q(\sqrt{3}, \sqrt{19})\)	\(\Q(\sqrt{-19}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}\cdot 5^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{7}+9q^{9}+(1-\beta _{3})q^{11}+(\beta _{1}+\cdots)q^{17}+\cdots\)
1900.3.e.e	$1900$	$3$	1900.e	19.b	$2$	$12$	$12$	$51.771$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{22}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{3}+\beta _{8}q^{7}+(-6-\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
1900.3.e.f	$1900$	$3$	1900.e	19.b	$2$	$12$	$12$	$51.771$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(12\)	$2^{12}\cdot 5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(1+\beta _{9})q^{7}+(-1+\beta _{2})q^{9}+\cdots\)
1900.3.e.g	$1900$	$3$	1900.e	19.b	$2$	$14$	$14$	$51.771$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{7}q^{7}+(-4+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots\)
1900.3.e.h	$1900$	$3$	1900.e	19.b	$2$	$14$	$14$	$51.771$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$5$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{7}q^{7}+(-4+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)