Space of modular forms of level 104, weight 2, and Character 104.e

• Label: 104.2.e
• Level: $104$
• Weight: $2$
• Character orbit: 104.e
• Rep. character: $\chi_{104}(77,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $28$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(28\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(104, [\chi])\).

	Total	New	Old
Modular forms	16	16	0
Cusp forms	12	12	0
Eisenstein series	4	4	0

Trace form

\( 12 q - 2 q^{4} - 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(104, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
104.2.e.a	$104$	$2$	104.e	104.e	$2$	$2$	$2$	$0.830$	\(\Q(\sqrt{-1}) \)	None		✓			104.2.e.a	$2$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-1)q^{2}-i q^{3}-2 i q^{4}+q^{5}+\cdots\)
104.2.e.b	$104$	$2$	104.e	104.e	$2$	$2$	$2$	$0.830$	\(\Q(\sqrt{-1}) \)	None		✓			104.2.e.a	$2$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i+1)q^{2}+i q^{3}+2 i q^{4}-q^{5}+\cdots\)
104.2.e.c	$104$	$2$	104.e	104.e	$2$	$8$	$8$	$0.830$	8.0.4521217600.1	None		✓	✓		104.2.e.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{3}-\beta _{5}q^{4}-\beta _{6}q^{5}+\cdots\)