Space of modular forms of level 23, weight 13, and Character 23.b

• Label: 23.13.b
• Level: $23$
• Weight: $13$
• Character orbit: 23.b
• Rep. character: $\chi_{23}(22,\cdot)$
• Character field: $\Q$
• Dimension: $23$
• Newform subspaces: $3$
• Sturm bound: $26$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$23$
Weight:	$k$	$=$	$13$
Character orbit:	$[\chi]$	$=$	23.b (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$23$
Character field:			$\Q$
Newform subspaces:			$3$
Sturm bound:			$26$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{13}(23, [\chi])$.

	Total	New	Old
Modular forms	25	25	0
Cusp forms	23	23	0
Eisenstein series	2	2	0

Trace form

23 * q + 88 * q^2 + 318 * q^3 + 48360 * q^4 + 45651 * q^6 + 665411 * q^8 + 3565749 * q^9 + 2474859 * q^12 + 8049118 * q^13 + 132075280 * q^16 + 159082899 * q^18 + 76917959 * q^23 - 364991808 * q^24 - 1091895337 * q^25 - 764362597 * q^26 - 1698209844 * q^27 - 417897362 * q^29 - 1574125298 * q^31 + 7111022304 * q^32 + 4723363152 * q^35 + 13003973139 * q^36 - 7972710324 * q^39 - 132511250 * q^41 + 62599086544 * q^46 - 45052376402 * q^47 - 27147783645 * q^48 - 24010321657 * q^49 - 57446928200 * q^50 + 59410714059 * q^52 - 131249166093 * q^54 - 12572534832 * q^55 - 49404502069 * q^58 - 169959852866 * q^59 + 266541022211 * q^62 + 492270216707 * q^64 + 7914588558 * q^69 + 590935322064 * q^70 - 40523102210 * q^71 + 725416146243 * q^72 - 449748966242 * q^73 + 2570431278 * q^75 - 345974135760 * q^77 - 1383271429293 * q^78 - 1847691172701 * q^81 - 1172318884789 * q^82 + 1051198266576 * q^85 + 313947423036 * q^87 + 3755301759672 * q^92 + 1120227951516 * q^93 + 22074265235 * q^94 + 3777482201184 * q^95 - 4724527700397 * q^96 + 3590387133208 * q^98

Decomposition of $S_{13}^{\mathrm{new}}(23, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
23.13.b.a	$23$	$13$	23.b	23.b	$2$	$1$	$1$	$21.022$	$\Q$	$\Q(\sqrt{-23})$	✓	✓			23.13.b.a	$2$	$0$	$-79$	$-14$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-79q^{2}-14q^{3}+2145q^{4}+1106q^{6}+\cdots$
23.13.b.b	$23$	$13$	23.b	23.b	$2$	$2$	$2$	$21.022$	$\Q(\sqrt{69})$	$\Q(\sqrt{-23})$	✓	✓			23.13.b.b	$2$	$0$	$79$	$14$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+(29+21\beta )q^{2}+(159-304\beta )q^{3}+\cdots$
23.13.b.c	$23$	$13$	23.b	23.b	$2$	$20$	$20$	$21.022$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	None		✓	✓		23.13.b.c	$2$	$0$	$88$	$318$	$0$	$0$	$2^{35}\cdot 3^{11}\cdot 67$	$\mathrm{SU}(2)[C_{2}]$	$q+(4+\beta _{1})q^{2}+(15+2\beta _{1}-\beta _{3})q^{3}+\cdots$