Space of modular forms of level 104, weight 3, and Character 104.v

• Label: 104.3.v
• Level: $104$
• Weight: $3$
• Character orbit: 104.v
• Rep. character: $\chi_{104}(33,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $28$
• Newform subspaces: $4$
• Sturm bound: $42$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	104.v (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(42\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(104, [\chi])\).

	Total	New	Old
Modular forms	128	28	100
Cusp forms	96	28	68
Eisenstein series	32	0	32

Trace form

\( 28 q + 2 q^{5} - 16 q^{7} - 42 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(104, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
104.3.v.a	$104$	$3$	104.v	13.f	$12$	$4$	$1$	$2.834$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}+2\zeta_{12}^{2}+\zeta_{12}^{3})q^{3}+(3+6\zeta_{12}+\cdots)q^{5}+\cdots\)
104.3.v.b	$104$	$3$	104.v	13.f	$12$	$4$	$1$	$2.834$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(4\)	\(6\)	\(16\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2\zeta_{12}+2\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+\cdots\)
104.3.v.c	$104$	$3$	104.v	13.f	$12$	$8$	$2$	$2.834$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(-8\)	\(-2\)	\(-36\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-2-\beta _{2}-2\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
104.3.v.d	$104$	$3$	104.v	13.f	$12$	$12$	$3$	$2.834$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(6\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{7}q^{3}+(-1+\beta _{2}-\beta _{3}+2\beta _{4}+2\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(104, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(104, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)