Space of modular forms of level 17, weight 10, and Character 17.b

• Label: 17.10.b
• Level: $17$
• Weight: $10$
• Character orbit: 17.b
• Rep. character: $\chi_{17}(16,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(17, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	12	12	0
Eisenstein series	2	2	0

Trace form

12 * q + 30 * q^2 + 1874 * q^4 + 23550 * q^8 - 9184 * q^9 - 63204 * q^13 - 243480 * q^15 + 38978 * q^16 - 105960 * q^17 + 547706 * q^18 + 1110672 * q^19 - 172580 * q^21 - 4441796 * q^25 + 1336332 * q^26 - 500496 * q^30 - 1934850 * q^32 - 6557404 * q^33 - 15085546 * q^34 + 3519864 * q^35 + 30244102 * q^36 + 28748136 * q^38 - 11901296 * q^42 + 10004616 * q^43 - 112552440 * q^47 + 121354720 * q^49 - 164889018 * q^50 - 52506472 * q^51 - 59093180 * q^52 + 76804272 * q^53 + 300732568 * q^55 + 11618904 * q^59 + 101609232 * q^60 - 260062974 * q^64 + 18429632 * q^66 - 304208752 * q^67 - 444301206 * q^68 - 211308236 * q^69 + 460311456 * q^70 + 493218954 * q^72 + 416024248 * q^76 + 138357828 * q^77 - 363335792 * q^81 - 845042136 * q^83 + 958037984 * q^84 - 388949632 * q^85 + 127952904 * q^86 + 610860648 * q^87 - 938223804 * q^89 + 1635779524 * q^93 - 238629952 * q^94 - 152046078 * q^98

Decomposition of \(S_{10}^{\mathrm{new}}(17, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
17.10.b.a	$17$	$10$	17.b	17.b	$2$	$12$	$12$	$8.756$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓	✓	17.10.b.a	$2$	$0$	\(30\)	\(0\)	\(0\)	\(0\)	$2^{17}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta _{2})q^{2}+\beta _{1}q^{3}+(154+4\beta _{2}+\cdots)q^{4}+\cdots\)