Space of modular forms of level 15, weight 13, and Character 15.d

• Label: 15.13.d
• Level: $15$
• Weight: $13$
• Character orbit: 15.d
• Rep. character: $\chi_{15}(14,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $3$
• Sturm bound: $26$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	15.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(26\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(15, [\chi])\).

	Total	New	Old
Modular forms	26	26	0
Cusp forms	22	22	0
Eisenstein series	4	4	0

Trace form

22 * q + 41418 * q^4 + 31230 * q^6 - 185202 * q^9 - 1102990 * q^10 + 5890590 * q^15 + 23549522 * q^16 + 62359196 * q^19 - 35764056 * q^21 - 178470630 * q^24 + 73756390 * q^25 - 133304220 * q^30 + 2005341404 * q^31 - 2095837340 * q^34 - 4834105758 * q^36 + 844454016 * q^39 - 5339087870 * q^40 + 25601716440 * q^45 + 36277077100 * q^46 - 37184673146 * q^49 - 67072796100 * q^51 + 60885269190 * q^54 - 87477714720 * q^55 + 206576808210 * q^60 + 342179846204 * q^61 - 227817519422 * q^64 - 714113270640 * q^66 + 269792074260 * q^69 - 571010393160 * q^70 + 741897954720 * q^75 + 1478373874884 * q^76 - 161650343524 * q^79 - 1533120298938 * q^81 + 451094419656 * q^84 - 1458492546820 * q^85 + 1239010468290 * q^90 + 1362052827648 * q^91 - 37217913380 * q^94 - 940207710510 * q^96 + 870539741280 * q^99

Decomposition of \(S_{13}^{\mathrm{new}}(15, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.13.d.a	$15$	$13$	15.d	15.d	$2$	$1$	$1$	$13.710$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	✓			15.13.d.a	$2$	$0$	\(-7\)	\(729\)	\(15625\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-7q^{2}+3^{6}q^{3}-4047q^{4}+5^{6}q^{5}+\cdots\)
15.13.d.b	$15$	$13$	15.d	15.d	$2$	$1$	$1$	$13.710$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	✓			15.13.d.a	$2$	$0$	\(7\)	\(-729\)	\(-15625\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+7q^{2}-3^{6}q^{3}-4047q^{4}-5^{6}q^{5}+\cdots\)
15.13.d.c	$15$	$13$	15.d	15.d	$2$	$20$	$20$	$13.710$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓		15.13.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{32}\cdot 3^{44}\cdot 5^{19}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{4}q^{2}+\beta _{1}q^{3}+(2476+\beta _{2})q^{4}+\cdots\)