Space of modular forms of level 104, weight 1, and Character 104.h

• Label: 104.1.h
• Level: $104$
• Weight: $1$
• Character orbit: 104.h
• Rep. character: $\chi_{104}(51,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $14$
• Trace bound: $2$

Defining parameters

Level:	$N$	$=$	$104 = 2^{3} \cdot 13$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	104.h (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$104$
Character field:			$\Q$
Newform subspaces:			$2$
Sturm bound:			$14$
Trace bound:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{1}(104, [\chi])$.

	Total	New	Old
Modular forms	4	4	0
Cusp forms	2	2	0
Eisenstein series	2	2	0

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

	$D_n$	$A_4$	$S_4$	$A_5$
Dimension	2	0	0	0

Trace form

2 * q - 2 * q^3 + 2 * q^4 - 2 * q^10 - 2 * q^12 - 2 * q^14 + 2 * q^16 - 2 * q^17 + 2 * q^26 + 2 * q^27 + 2 * q^30 + 2 * q^35 - 2 * q^40 + 2 * q^42 - 2 * q^43 - 2 * q^48 + 2 * q^51 - 2 * q^56 + 4 * q^62 + 2 * q^64 - 2 * q^65 - 2 * q^68 - 2 * q^74 - 2 * q^78 - 2 * q^81 - 2 * q^91 - 2 * q^94

Decomposition of $S_{1}^{\mathrm{new}}(104, [\chi])$ 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
104.1.h.a	$104$	$1$	104.h	104.h	$2$	$1$	$1$	$0.052$	$\Q$	$D_{3}$	$\Q(\sqrt{-26})$	None	✓	✓			104.1.h.a	$2$	$0$	$-1$	$-1$	$1$	$1$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
104.1.h.b	$104$	$1$	104.h	104.h	$2$	$1$	$1$	$0.052$	$\Q$	$D_{3}$	$\Q(\sqrt{-26})$	None	✓	✓			104.1.h.a	$2$	$0$	$1$	$-1$	$-1$	$-1$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$