Space of modular forms of level 2511, weight 1, and Character 2511.m

• Label: 2511.1.m
• Level: $2511$
• Weight: $1$
• Character orbit: 2511.m
• Rep. character: $\chi_{2511}(433,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $38$
• Newform subspaces: $9$
• Sturm bound: $288$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 2511 = 3^{4} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2511.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 279 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(288\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2511, [\chi])\).

	Total	New	Old
Modular forms	62	42	20
Cusp forms	38	38	0
Eisenstein series	24	4	20

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	38	0	0	0

Trace form

\( 38 q - 13 q^{4} + 4 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2511, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2511.1.m.a	$2511$	$1$	2511.m	279.m	$6$	$2$	$1$	$1.253$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-31}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(-1\)	\(1\)	$1$		\(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}-q^{8}+\cdots\)
2511.1.m.b	$2511$	$1$	2511.m	279.m	$6$	$2$	$1$	$1.253$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-31}) \)	\(\Q(\sqrt{93}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+\zeta_{6}q^{4}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{16}-q^{19}+\cdots\)
2511.1.m.c	$2511$	$1$	2511.m	279.m	$6$	$2$	$1$	$1.253$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{93}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}+(-1-\zeta_{6})q^{11}+\cdots\)
2511.1.m.d	$2511$	$1$	2511.m	279.m	$6$	$2$	$1$	$1.253$	\(\Q(\sqrt{-3}) \)	$D_{6}$	None	\(\Q(\sqrt{93}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(1\)	$1$		\(q+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}+(1+\zeta_{6})q^{11}+\zeta_{6}^{2}q^{16}+\cdots\)
2511.1.m.e	$2511$	$1$	2511.m	279.m	$6$	$2$	$1$	$1.253$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-31}) \)	None		$4$	$0$	\(1\)	\(0\)	\(1\)	\(1\)	$1$		\(q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+q^{8}+\cdots\)
2511.1.m.f	$2511$	$1$	2511.m	279.m	$6$	$4$	$2$	$1.253$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-31}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$3$		\(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(-1+\zeta_{12}^{2}+\zeta_{12}^{4}+\cdots)q^{4}+\cdots\)
2511.1.m.g	$2511$	$1$	2511.m	279.m	$6$	$6$	$3$	$1.253$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-31}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$		\(q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{4}+\cdots\)
2511.1.m.h	$2511$	$1$	2511.m	279.m	$6$	$6$	$3$	$1.253$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-31}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$		\(q+(-\zeta_{18}^{2}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{4}+\zeta_{18}^{6}+\cdots)q^{4}+\cdots\)
2511.1.m.i	$2511$	$1$	2511.m	279.m	$6$	$12$	$6$	$1.253$	\(\Q(\zeta_{36})\)	$D_{18}$	\(\Q(\sqrt{-31}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{3}$		\(q+(\zeta_{36}^{5}+\zeta_{36}^{7})q^{2}+(\zeta_{36}^{10}+\zeta_{36}^{12}+\cdots)q^{4}+\cdots\)