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

• Label: 104.2.s
• Level: $104$
• Weight: $2$
• Character orbit: 104.s
• Rep. character: $\chi_{104}(69,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• 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.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(28\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	32	32	0
Cusp forms	24	24	0
Eisenstein series	8	8	0

Trace form

24 * q - 3 * q^2 - q^4 + 6 * q^6 - 6 * q^7 + 6 * q^9 + q^10 - 8 * q^12 - 24 * q^15 - 9 * q^16 - 4 * q^17 - 27 * q^20 + 18 * q^22 - 14 * q^23 - 36 * q^24 + 4 * q^25 + 29 * q^26 - 12 * q^30 - 3 * q^32 - 6 * q^33 + 9 * q^36 + 14 * q^39 - 6 * q^40 - 12 * q^41 + 14 * q^42 + 42 * q^46 + 30 * q^48 + 6 * q^49 + 18 * q^50 + 36 * q^52 - 18 * q^54 + 20 * q^55 - 8 * q^56 - 15 * q^58 - 4 * q^62 - 24 * q^63 + 50 * q^64 - 30 * q^65 + 8 * q^66 + 29 * q^68 - 6 * q^71 + 87 * q^72 - 35 * q^74 + 36 * q^76 - 68 * q^78 + 32 * q^79 + 15 * q^80 + 8 * q^81 + 19 * q^82 - 48 * q^84 + 22 * q^87 - 24 * q^88 - 6 * q^89 - 114 * q^90 + 68 * q^92 - 20 * q^94 + 40 * q^95 - 30 * q^97 - 123 * q^98

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.s.a	$104$	$2$	104.s	104.s	$6$	$4$	$2$	$0.830$	\(\Q(\zeta_{12})\)	None		✓			104.2.s.a	$2$	$1$	\(-4\)	\(-6\)	\(-8\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
104.2.s.b	$104$	$2$	104.s	104.s	$6$	$4$	$2$	$0.830$	\(\Q(\zeta_{12})\)	None		✓			104.2.s.a	$2$	$0$	\(-2\)	\(6\)	\(8\)	\(-12\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}+\cdots)q^{3}+\cdots\)
104.2.s.c	$104$	$2$	104.s	104.s	$6$	$16$	$8$	$0.830$	16.0.\(\cdots\).2	None		✓	✓		104.2.s.c	$4$	$0$	\(3\)	\(0\)	\(0\)	\(18\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{14})q^{2}+(\beta _{3}-\beta _{11})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)