Space of modular forms of level 2915, weight 1, and Character 2915.e

• Label: 2915.1.e
• Level: $2915$
• Weight: $1$
• Character orbit: 2915.e
• Rep. character: $\chi_{2915}(2914,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $8$
• Sturm bound: $324$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 2915 = 5 \cdot 11 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2915.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 2915 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(324\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2915, [\chi])\).

	Total	New	Old
Modular forms	14	14	0
Cusp forms	10	10	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	10	0	0	0

Trace form

\( 10 q + 10 q^{4} + 6 q^{9} - 2 q^{11} - 4 q^{15} + 10 q^{16} + 10 q^{25} + 6 q^{36} - 2 q^{44} + 6 q^{49} - 4 q^{59} - 4 q^{60} + 10 q^{64} - 8 q^{69} + 2 q^{81} - 4 q^{89} - 8 q^{91} - 6 q^{99}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2915, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2915.1.e.a	$2915$	$1$	2915.e	2915.e	$2$	$1$	$1$	$1.455$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-2915}) \)	\(\Q(\sqrt{265}) \)	✓	✓			2915.1.e.a	$4$	$0$	\(0\)	\(-2\)	\(1\)	\(0\)	$1$		\(q-2q^{3}+q^{4}+q^{5}+3q^{9}-q^{11}-2q^{12}+\cdots\)
2915.1.e.b	$2915$	$1$	2915.e	2915.e	$2$	$1$	$1$	$1.455$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2915}) \)	None	✓	✓			2915.1.e.b	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(-1\)	$1$		\(q-q^{3}+q^{4}+q^{5}-q^{7}+q^{11}-q^{12}+\cdots\)
2915.1.e.c	$2915$	$1$	2915.e	2915.e	$2$	$1$	$1$	$1.455$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2915}) \)	None	✓	✓			2915.1.e.b	$2$	$0$	\(0\)	\(-1\)	\(1\)	\(1\)	$1$		\(q-q^{3}+q^{4}+q^{5}+q^{7}+q^{11}-q^{12}+\cdots\)
2915.1.e.d	$2915$	$1$	2915.e	2915.e	$2$	$1$	$1$	$1.455$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2915}) \)	None	✓	✓			2915.1.e.b	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(-1\)	$1$		\(q+q^{3}+q^{4}-q^{5}-q^{7}+q^{11}+q^{12}+\cdots\)
2915.1.e.e	$2915$	$1$	2915.e	2915.e	$2$	$1$	$1$	$1.455$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-2915}) \)	None	✓	✓			2915.1.e.b	$2$	$0$	\(0\)	\(1\)	\(-1\)	\(1\)	$1$		\(q+q^{3}+q^{4}-q^{5}+q^{7}+q^{11}+q^{12}+\cdots\)
2915.1.e.f	$2915$	$1$	2915.e	2915.e	$2$	$1$	$1$	$1.455$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-2915}) \)	\(\Q(\sqrt{265}) \)	✓	✓			2915.1.e.a	$4$	$0$	\(0\)	\(2\)	\(-1\)	\(0\)	$1$		\(q+2q^{3}+q^{4}-q^{5}+3q^{9}-q^{11}+2q^{12}+\cdots\)
2915.1.e.g	$2915$	$1$	2915.e	2915.e	$2$	$2$	$2$	$1.455$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-2915}) \)	None	✓	✓			2915.1.e.g	$4$	$0$	\(0\)	\(-2\)	\(-2\)	\(0\)	$1$		\(q-q^{3}+q^{4}-q^{5}-\beta q^{7}-q^{11}-q^{12}+\cdots\)
2915.1.e.h	$2915$	$1$	2915.e	2915.e	$2$	$2$	$2$	$1.455$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-2915}) \)	None	✓	✓			2915.1.e.g	$4$	$0$	\(0\)	\(2\)	\(2\)	\(0\)	$1$		\(q+q^{3}+q^{4}+q^{5}-\beta q^{7}-q^{11}+q^{12}+\cdots\)