Space of modular forms of level 1900, weight 1, and Character 1900.e

• Label: 1900.1.e
• Level: $1900$
• Weight: $1$
• Character orbit: 1900.e
• Rep. character: $\chi_{1900}(1101,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $300$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1900.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(300\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1900, [\chi])\).

	Total	New	Old
Modular forms	33	3	30
Cusp forms	15	3	12
Eisenstein series	18	0	18

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	3	0	0	0

Trace form

\( 3 q + q^{7} + 3 q^{9} + q^{11} + q^{17} - q^{19} - 2 q^{23} + q^{43} + q^{47} + 4 q^{49} + q^{61} + q^{63} + q^{73} - q^{77} + 3 q^{81} - 2 q^{83} + q^{99}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1900.1.e.a	$1900$	$1$	1900.e	19.b	$2$	$1$	$1$	$0.948$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-19}) \)	None	✓				76.1.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q+q^{7}+q^{9}-q^{11}+q^{17}+q^{19}-2q^{23}+\cdots\)
1900.1.e.b	$1900$	$1$	1900.e	19.b	$2$	$2$	$2$	$0.948$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-19}) \)	None	✓		✓		380.1.g.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{7}+q^{9}+q^{11}+\beta q^{17}-q^{19}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1900, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)