Space of modular forms of level 15, weight 11, and Character 15.d

• Label: 15.11.d
• Level: $15$
• Weight: $11$
• Character orbit: 15.d
• Rep. character: $\chi_{15}(14,\cdot)$
• Character field: $\Q$
• Dimension: $18$
• Newform subspaces: $3$
• Sturm bound: $22$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
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:			\(22\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(15, [\chi])\).

	Total	New	Old
Modular forms	22	22	0
Cusp forms	18	18	0
Eisenstein series	4	4	0

Trace form

18 * q + 7578 * q^4 - 8130 * q^6 + 55098 * q^9 + 159570 * q^10 - 787110 * q^15 + 2708658 * q^16 + 948996 * q^19 + 2444616 * q^21 - 21576390 * q^24 + 10206450 * q^25 - 35678700 * q^30 - 59273964 * q^31 - 43261740 * q^34 + 296165538 * q^36 - 70953984 * q^39 + 457865010 * q^40 - 484245000 * q^45 - 1408002660 * q^46 + 654049314 * q^49 + 1862294820 * q^51 - 1309470570 * q^54 + 1424671200 * q^55 - 3485977470 * q^60 - 2627395164 * q^61 + 1760137938 * q^64 + 2368350000 * q^66 + 2415438780 * q^69 + 2838634200 * q^70 - 1285884000 * q^75 + 2626752276 * q^76 - 6395297004 * q^79 - 4403113182 * q^81 + 13119851016 * q^84 - 7022493180 * q^85 + 7290143730 * q^90 + 19275224832 * q^91 - 47407059540 * q^94 - 57890902590 * q^96 + 42957756000 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(15, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.11.d.a	$15$	$11$	15.d	15.d	$2$	$1$	$1$	$9.530$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	✓			15.11.d.a	$2$	$0$	\(-61\)	\(243\)	\(-3125\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-61q^{2}+3^{5}q^{3}+2697q^{4}-5^{5}q^{5}+\cdots\)
15.11.d.b	$15$	$11$	15.d	15.d	$2$	$1$	$1$	$9.530$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	✓			15.11.d.a	$2$	$0$	\(61\)	\(-243\)	\(3125\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+61q^{2}-3^{5}q^{3}+2697q^{4}+5^{5}q^{5}+\cdots\)
15.11.d.c	$15$	$11$	15.d	15.d	$2$	$16$	$16$	$9.530$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		15.11.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}\cdot 3^{32}\cdot 5^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+(-\beta _{6}+\beta _{7})q^{3}+(137-\beta _{2}+\cdots)q^{4}+\cdots\)