Space of modular forms of level 117, weight 10, and Character 117.i

• Label: 117.10.i
• Level: $117$
• Weight: $10$
• Character orbit: 117.i
• Rep. character: $\chi_{117}(8,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $84$
• Newform subspaces: $1$
• Sturm bound: $140$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	117.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(140\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(117, [\chi])\).

	Total	New	Old
Modular forms	260	84	176
Cusp forms	244	84	160
Eisenstein series	16	0	16

Trace form

84 * q - 3648 * q^7 + 2916 * q^13 - 4190448 * q^16 + 1316544 * q^19 + 1517616 * q^22 + 7370184 * q^28 + 14352960 * q^31 - 47891880 * q^34 - 25672020 * q^37 + 250007616 * q^40 + 213738984 * q^46 - 5535744 * q^52 + 175898304 * q^55 - 398581488 * q^58 - 557705880 * q^61 - 102866592 * q^67 - 492819192 * q^70 - 1597680228 * q^73 + 3530118696 * q^76 + 180627408 * q^79 - 2547796536 * q^85 + 1033419408 * q^91 - 6733876032 * q^94 + 3652225284 * q^97

Decomposition of \(S_{10}^{\mathrm{new}}(117, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
117.10.i.a	$117$	$10$	117.i	39.f	$4$	$84$	$42$	$60.259$		None		✓	✓	✓	117.10.i.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-3648\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{10}^{\mathrm{old}}(117, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(117, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 2}\)