Space of modular forms of level 2695, weight 1, and Character 2695.g

• Label: 2695.1.g
• Level: $2695$
• Weight: $1$
• Character orbit: 2695.g
• Rep. character: $\chi_{2695}(1814,\cdot)$
• Character field: $\Q$
• Dimension: $15$
• Newform subspaces: $9$
• Sturm bound: $336$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2695.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(336\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2695, [\chi])\).

	Total	New	Old
Modular forms	34	25	9
Cusp forms	18	15	3
Eisenstein series	16	10	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	15	0	0	0

Trace form

15 * q + q^4 + q^5 - q^9 + q^11 + 7 * q^16 - q^20 + 7 * q^25 + 2 * q^31 + 17 * q^36 - 9 * q^44 + q^45 - q^55 - 2 * q^59 - 7 * q^64 - 10 * q^71 + q^80 + 15 * q^81 - 8 * q^86 + 2 * q^89 + q^99

Decomposition of \(S_{1}^{\mathrm{new}}(2695, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2695.1.g.a	$2695$	$1$	2695.g	55.d	$2$	$1$	$1$	$1.345$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-55}) \)	None	✓				385.1.q.a	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-q^{2}-q^{5}+q^{8}+q^{9}+q^{10}+q^{11}+\cdots\)
2695.1.g.b	$2695$	$1$	2695.g	55.d	$2$	$1$	$1$	$1.345$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-55}) \)	None	✓				385.1.q.a	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q-q^{2}+q^{5}+q^{8}+q^{9}-q^{10}+q^{11}+\cdots\)
2695.1.g.c	$2695$	$1$	2695.g	55.d	$2$	$1$	$1$	$1.345$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{5}) \)	✓				55.1.d.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q-q^{4}+q^{5}+q^{9}-q^{11}+q^{16}-q^{20}+\cdots\)
2695.1.g.d	$2695$	$1$	2695.g	55.d	$2$	$1$	$1$	$1.345$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-55}) \)	None	✓				385.1.q.a	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+q^{2}-q^{5}-q^{8}+q^{9}-q^{10}+q^{11}+\cdots\)
2695.1.g.e	$2695$	$1$	2695.g	55.d	$2$	$1$	$1$	$1.345$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-55}) \)	None	✓				385.1.q.a	$2$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+q^{2}+q^{5}-q^{8}+q^{9}+q^{10}+q^{11}+\cdots\)
2695.1.g.f	$2695$	$1$	2695.g	55.d	$2$	$2$	$2$	$1.345$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-35}) \)	\(\Q(\sqrt{385}) \)		✓			2695.1.g.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-2 i q^{3}-q^{4}-i q^{5}-3 q^{9}-q^{11}+\cdots\)
2695.1.g.g	$2695$	$1$	2695.g	55.d	$2$	$2$	$2$	$1.345$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-55}) \)	None	✓				385.1.q.c	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q-\beta q^{2}+2q^{4}-q^{5}-\beta q^{8}+q^{9}+\beta q^{10}+\cdots\)
2695.1.g.h	$2695$	$1$	2695.g	55.d	$2$	$2$	$2$	$1.345$	\(\Q(\sqrt{3}) \)	$D_{6}$	\(\Q(\sqrt{-55}) \)	None	✓				385.1.q.c	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-\beta q^{2}+2q^{4}+q^{5}-\beta q^{8}+q^{9}-\beta q^{10}+\cdots\)
2695.1.g.i	$2695$	$1$	2695.g	55.d	$2$	$4$	$4$	$1.345$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-11}) \)	None		✓	✓		2695.1.g.i	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{8}+\zeta_{8}^{3})q^{3}-q^{4}-\zeta_{8}q^{5}-q^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2695, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2695, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 3}\)