Space of modular forms of level 104, weight 10, and Character 104.i

• Label: 104.10.i
• Level: $104$
• Weight: $10$
• Character orbit: 104.i
• Rep. character: $\chi_{104}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $62$
• Newform subspaces: $2$
• Sturm bound: $140$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 104 = 2^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(140\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(104, [\chi])\).

	Total	New	Old
Modular forms	260	62	198
Cusp forms	244	62	182
Eisenstein series	16	0	16

Trace form

62 * q - 162 * q^3 - 122 * q^5 + 1026 * q^7 - 190269 * q^9 + 28462 * q^11 + 160275 * q^13 - 294712 * q^15 + 89491 * q^17 + 363562 * q^19 + 1067660 * q^21 - 1226070 * q^23 + 19828132 * q^25 + 9616164 * q^27 + 5937475 * q^29 + 11721712 * q^31 + 2311862 * q^33 - 11987624 * q^35 + 5237743 * q^37 + 40037782 * q^39 - 15715969 * q^41 + 8904126 * q^43 + 54782877 * q^45 - 133815128 * q^47 - 199950673 * q^49 - 84803364 * q^51 - 259067146 * q^53 - 134480088 * q^55 - 270788484 * q^57 - 55418294 * q^59 + 250137491 * q^61 + 342108168 * q^63 - 122876515 * q^65 + 198357210 * q^67 + 230209430 * q^69 + 577939538 * q^71 + 437516646 * q^73 - 520808602 * q^75 + 688053964 * q^77 - 396742440 * q^79 - 357518959 * q^81 + 2205240544 * q^83 + 1300296399 * q^85 + 348429778 * q^87 - 717685744 * q^89 - 786999186 * q^91 + 1287038128 * q^93 + 224492616 * q^95 - 1930161288 * q^97 + 225400784 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(104, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
104.10.i.a	$104$	$10$	104.i	13.c	$3$	$30$	$15$	$53.564$		None		✓			104.10.i.a	$2$	$0$	\(0\)	\(-81\)	\(-168\)	\(-5175\)		$\mathrm{SU}(2)[C_{3}]$
104.10.i.b	$104$	$10$	104.i	13.c	$3$	$32$	$16$	$53.564$		None		✓	✓		104.10.i.b	$2$	$0$	\(0\)	\(-81\)	\(46\)	\(6201\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{10}^{\mathrm{old}}(104, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(104, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)