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

• Label: 15.15.d
• Level: $15$
• Weight: $15$
• Character orbit: 15.d
• Rep. character: $\chi_{15}(14,\cdot)$
• Character field: $\Q$
• Dimension: $26$
• Newform subspaces: $3$
• Sturm bound: $30$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 15 \)
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:			\(30\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	30	30	0
Cusp forms	26	26	0
Eisenstein series	4	4	0

Trace form

\( 26 q + 203130 q^{4} - 129282 q^{6} + 4698018 q^{9} + O(q^{10}) \)

Decomposition of \(S_{15}^{\mathrm{new}}(15, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.15.d.a	$15$	$15$	15.d	15.d	$2$	$1$	$1$	$18.649$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	✓			15.15.d.a	$2$	$0$	\(-251\)	\(-2187\)	\(78125\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-251q^{2}-3^{7}q^{3}+46617q^{4}+5^{7}q^{5}+\cdots\)
15.15.d.b	$15$	$15$	15.d	15.d	$2$	$1$	$1$	$18.649$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	✓			15.15.d.a	$2$	$0$	\(251\)	\(2187\)	\(-78125\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+251q^{2}+3^{7}q^{3}+46617q^{4}-5^{7}q^{5}+\cdots\)
15.15.d.c	$15$	$15$	15.d	15.d	$2$	$24$	$24$	$18.649$		None		✓	✓		15.15.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$