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 - 2 * q^11 - q^13 + 8 * q^15 + 7 * q^17 - 6 * q^19 - 20 * q^21 - 6 * q^23 + 4 * q^25 + 4 * q^27 + 7 * q^29 - 16 * q^31 - 10 * q^33 - 8 * q^35 + 3 * q^37 + 6 * q^39 - 13 * q^41 - 2 * q^43 + 17 * q^45 + 40 * q^47 + 11 * q^49 - 4 * q^51 + 14 * q^53 + 8 * q^55 - 4 * q^57 + 10 * q^59 + 7 * q^61 + 8 * q^63 - 31 * q^65 + 26 * q^67 + 22 * q^69 + 2 * q^71 - 34 * q^73 - 26 * q^75 - 20 * q^77 - 40 * q^79 + 13 * q^81 - 32 * q^83 - 21 * q^85 + 2 * q^87 + 8 * q^89 + 30 * q^91 - 24 * q^95 + 16 * q^97 + 16 * q^99

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.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

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