Space of modular forms of level 105, weight 3, and Character 105.e

• Label: 105.3.e
• Level: $105$
• Weight: $3$
• Character orbit: 105.e
• Rep. character: $\chi_{105}(34,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(105, [\chi])\).

	Total	New	Old
Modular forms	36	16	20
Cusp forms	28	16	12
Eisenstein series	8	0	8

Trace form

16 * q - 32 * q^4 + 48 * q^9 - 56 * q^11 - 84 * q^14 + 24 * q^15 + 112 * q^16 - 12 * q^21 + 16 * q^25 - 32 * q^29 - 72 * q^30 - 4 * q^35 - 96 * q^36 + 72 * q^39 + 568 * q^44 - 96 * q^46 - 152 * q^49 - 96 * q^50 + 24 * q^51 + 444 * q^56 - 288 * q^60 - 992 * q^64 - 296 * q^65 + 504 * q^70 - 56 * q^71 - 48 * q^74 + 464 * q^79 + 144 * q^81 + 228 * q^84 + 608 * q^85 - 456 * q^86 - 88 * q^91 - 24 * q^95 - 168 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(105, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
105.3.e.a	$105$	$3$	105.e	35.c	$2$	$16$	$16$	$2.861$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓	✓	105.3.e.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}+\beta _{2}q^{3}+(-2+\beta _{4})q^{4}+(-\beta _{8}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(105, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)