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

• Label: 2695.1.q
• Level: $2695$
• Weight: $1$
• Character orbit: 2695.q
• Rep. character: $\chi_{2695}(2419,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $7$
• Sturm bound: $336$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2695.q (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 385 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
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	72	40	32
Cusp forms	40	24	16
Eisenstein series	32	16	16

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q + 4 q^{4} + 4 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2695.1.q.a	$2695$	$1$	2695.q	385.q	$6$	$2$	$1$	$1.345$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-55}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}q^{5}-q^{8}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{10}+\cdots\)
2695.1.q.b	$2695$	$1$	2695.q	385.q	$6$	$2$	$1$	$1.345$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{5}) \)		$8$	$0$	\(0\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots\)
2695.1.q.c	$2695$	$1$	2695.q	385.q	$6$	$2$	$1$	$1.345$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \)	\(\Q(\sqrt{5}) \)		$8$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots\)
2695.1.q.d	$2695$	$1$	2695.q	385.q	$6$	$2$	$1$	$1.345$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-55}) \)	None		$4$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}q^{5}+q^{8}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{10}+\cdots\)
2695.1.q.e	$2695$	$1$	2695.q	385.q	$6$	$4$	$2$	$1.345$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-55}) \)	None		$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$3$		\(q+(\zeta_{12}^{3}+\zeta_{12}^{5})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
2695.1.q.f	$2695$	$1$	2695.q	385.q	$6$	$4$	$2$	$1.345$	\(\Q(\zeta_{12})\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-35}) \)	\(\Q(\sqrt{385}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}q^{5}-3\zeta_{12}^{4}q^{9}+\cdots\)
2695.1.q.g	$2695$	$1$	2695.q	385.q	$6$	$8$	$4$	$1.345$	\(\Q(\zeta_{24})\)	$D_{4}$	\(\Q(\sqrt{-11}) \)	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{24}+\zeta_{24}^{7})q^{3}+\zeta_{24}^{4}q^{4}-\zeta_{24}^{5}q^{5}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(2695, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)