Space of modular forms of level 104, weight 4, and Character 104.e

• Label: 104.4.e
• Level: $104$
• Weight: $4$
• Character orbit: 104.e
• Rep. character: $\chi_{104}(77,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $1$
• Sturm bound: $56$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	104.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(56\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(104, [\chi])\).

	Total	New	Old
Modular forms	44	44	0
Cusp forms	40	40	0
Eisenstein series	4	4	0

Trace form

40 * q - 2 * q^4 - 328 * q^9 + 18 * q^10 + 118 * q^12 + 118 * q^14 + 90 * q^16 + 48 * q^17 - 508 * q^22 - 280 * q^23 + 752 * q^25 + 70 * q^26 - 58 * q^30 - 444 * q^36 + 292 * q^38 + 352 * q^39 + 1262 * q^40 + 446 * q^42 - 2530 * q^48 - 2096 * q^49 + 364 * q^52 + 232 * q^55 + 630 * q^56 + 96 * q^62 + 2794 * q^64 - 600 * q^65 - 560 * q^66 - 58 * q^68 + 3770 * q^74 + 610 * q^78 - 1584 * q^79 + 2048 * q^81 - 2136 * q^82 + 6248 * q^87 - 2480 * q^88 - 8488 * q^90 - 888 * q^92 - 3042 * q^94 + 1296 * q^95

Decomposition of \(S_{4}^{\mathrm{new}}(104, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
104.4.e.a	$104$	$4$	104.e	104.e	$2$	$40$	$40$	$6.136$		None		✓	✓	✓	104.4.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$