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

• Label: 104.2.i
• Level: $104$
• Weight: $2$
• Character orbit: 104.i
• Rep. character: $\chi_{104}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	104.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
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	36	6	30
Cusp forms	20	6	14
Eisenstein series	16	0	16

Trace form

\( 6 q - 2 q^{3} - 2 q^{5} + 2 q^{7} - q^{9} + O(q^{10}) \)

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	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
104.2.i.a	$104$	$2$	104.i	13.c	$3$	$2$	$1$	$0.830$	\(\Q(\sqrt{-3}) \)	None		✓	104.2.i.a	$2$	$0$	\(0\)	\(-1\)	\(4\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{3}+2q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
104.2.i.b	$104$	$2$	104.i	13.c	$3$	$4$	$2$	$0.830$	\(\Q(\sqrt{-3}, \sqrt{17})\)	None		✓	104.2.i.b	$2$	$0$	\(0\)	\(-1\)	\(-6\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(104, [\chi])\) into lower level spaces

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