Space of modular forms of level 11, weight 13, and Character 11.b

• Label: 11.13.b
• Level: $11$
• Weight: $13$
• Character orbit: 11.b
• Rep. character: $\chi_{11}(10,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $2$
• Sturm bound: $13$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(13\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(11, [\chi])\).

	Total	New	Old
Modular forms	13	13	0
Cusp forms	11	11	0
Eisenstein series	2	2	0

Trace form

11 * q + 1078 * q^3 - 16252 * q^4 + 718 * q^5 + 2069017 * q^9 + 55187 * q^11 - 14054012 * q^12 - 15139368 * q^14 + 44633276 * q^15 + 34751624 * q^16 - 230969972 * q^20 + 83533560 * q^22 + 194754598 * q^23 - 18318567 * q^25 - 372191832 * q^26 + 604793116 * q^27 - 558946586 * q^31 - 4707508322 * q^33 + 7677299352 * q^34 - 8956453520 * q^36 + 4234573678 * q^37 + 11254769640 * q^38 - 32091748680 * q^42 + 13381283564 * q^44 + 9469999394 * q^45 - 3953618282 * q^47 + 9795367528 * q^48 + 7515576203 * q^49 + 300447718 * q^53 - 31361369402 * q^55 + 82892128176 * q^56 - 84518430720 * q^58 - 10434876554 * q^59 - 142670045284 * q^60 + 163912403600 * q^64 + 322939363560 * q^66 - 87365524682 * q^67 + 530186104148 * q^69 - 382808641560 * q^70 - 499640014298 * q^71 - 556365875694 * q^75 + 425991883680 * q^77 - 483427126680 * q^78 + 715352833528 * q^80 + 227635214599 * q^81 + 625030365960 * q^82 - 1219447545552 * q^86 + 134692485840 * q^88 + 1615639304734 * q^89 + 1356772643808 * q^91 - 3736850161052 * q^92 + 77330788916 * q^93 - 4588979538722 * q^97 + 923150273881 * q^99

Decomposition of \(S_{13}^{\mathrm{new}}(11, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.13.b.a	$11$	$13$	11.b	11.b	$2$	$1$	$1$	$10.054$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	✓			11.13.b.a	$2$	$0$	\(0\)	\(-1358\)	\(-25774\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-1358q^{3}+2^{12}q^{4}-25774q^{5}+\cdots\)
11.13.b.b	$11$	$13$	11.b	11.b	$2$	$10$	$10$	$10.054$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		✓	✓		11.13.b.b	$2$	$0$	\(0\)	\(2436\)	\(26492\)	\(0\)	$2^{16}\cdot 3^{3}\cdot 11^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(244+\beta _{3})q^{3}+(-2035+\cdots)q^{4}+\cdots\)