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

• Label: 104.2.b
• Level: $104$
• Weight: $2$
• Character orbit: 104.b
• Rep. character: $\chi_{104}(53,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $28$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(28\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

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

Trace form

\( 12 q - 2 q^{2} - 2 q^{4} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 12 q^{9} + O(q^{10}) \)

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.b.a	$104$	$2$	104.b	8.b	$2$	$2$	$2$	$0.830$	\(\Q(\sqrt{-1}) \)	None		✓			104.2.b.a	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(i-1)q^{2}-i q^{3}-2 i q^{4}+3 i q^{5}+\cdots\)
104.2.b.b	$104$	$2$	104.b	8.b	$2$	$4$	$4$	$0.830$	\(\Q(\zeta_{12})\)	None		✓			104.2.b.b	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-12\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta_{2}+\beta_1)q^{2}+2\beta_{2} q^{3}+(\beta_{3}+\beta_1)q^{4}+\cdots\)
104.2.b.c	$104$	$2$	104.b	8.b	$2$	$6$	$6$	$0.830$	6.0.399424.1	None		✓	✓		104.2.b.c	$2$	$0$	\(-2\)	\(0\)	\(0\)	\(2\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)