Space of modular forms of level 3015, weight 1, and Character 3015.h

• Label: 3015.1.h
• Level: $3015$
• Weight: $1$
• Character orbit: 3015.h
• Rep. character: $\chi_{3015}(334,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $408$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3015 = 3^{2} \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3015.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 335 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(408\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3015, [\chi])\).

	Total	New	Old
Modular forms	40	10	30
Cusp forms	32	8	24
Eisenstein series	8	2	6

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q + 6 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3015, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3015.1.h.a	$3015$	$1$	3015.h	335.d	$2$	$1$	$1$	$1.505$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-335}) \)	None	✓		335.1.d.a	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(1\)	$1$		\(q-q^{2}+q^{5}+q^{7}+q^{8}-q^{10}-2q^{13}+\cdots\)
3015.1.h.b	$3015$	$1$	3015.h	335.d	$2$	$1$	$1$	$1.505$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-335}) \)	None	✓		335.1.d.a	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(-1\)	$1$		\(q+q^{2}-q^{5}-q^{7}-q^{8}-q^{10}+2q^{13}+\cdots\)
3015.1.h.c	$3015$	$1$	3015.h	335.d	$2$	$3$	$3$	$1.505$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-335}) \)	None	✓		335.1.d.c	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$1$		\(q+(-\beta _{1}+\beta _{2})q^{2}+(1-\beta _{1})q^{4}-q^{5}+\cdots\)
3015.1.h.d	$3015$	$1$	3015.h	335.d	$2$	$3$	$3$	$1.505$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-335}) \)	None	✓		335.1.d.c	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$		\(q+(\beta _{1}-\beta _{2})q^{2}+(1-\beta _{1})q^{4}+q^{5}+\beta _{1}q^{7}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3015, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3015, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(1005, [\chi])\)\(^{\oplus 2}\)