Space of modular forms of level 2151, weight 1, and Character 2151.d

• Label: 2151.1.d
• Level: $2151$
• Weight: $1$
• Character orbit: 2151.d
• Rep. character: $\chi_{2151}(955,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $5$
• Sturm bound: $240$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 2151 = 3^{2} \cdot 239 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2151.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 239 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(240\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2151, [\chi])\).

	Total	New	Old
Modular forms	36	12	24
Cusp forms	32	11	21
Eisenstein series	4	1	3

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	7	0	4	0

Trace form

\( 11 q + q^{2} + 6 q^{4} + q^{5} + 2 q^{8} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2151, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2151.1.d.a	$2151$	$1$	2151.d	239.b	$2$	$1$	$1$	$1.073$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-239}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+q^{2}+q^{5}-q^{8}+q^{10}+q^{11}-q^{16}+\cdots\)
2151.1.d.b	$2151$	$1$	2151.d	239.b	$2$	$2$	$2$	$1.073$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)	$1$		\(q-q^{2}+q^{5}-\beta q^{7}+q^{8}-q^{10}+q^{11}+\cdots\)
2151.1.d.c	$2151$	$1$	2151.d	239.b	$2$	$2$	$2$	$1.073$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-239}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+(1-\beta )q^{2}+(1-\beta )q^{4}+(1-\beta )q^{5}+\cdots\)
2151.1.d.d	$2151$	$1$	2151.d	239.b	$2$	$2$	$2$	$1.073$	\(\Q(\sqrt{-2}) \)	$S_{4}$	None	None		$2$	$0$	\(2\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+q^{2}-q^{5}-\beta q^{7}-q^{8}-q^{10}-q^{11}+\cdots\)
2151.1.d.e	$2151$	$1$	2151.d	239.b	$2$	$4$	$4$	$1.073$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-239}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2151, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2151, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(239, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(717, [\chi])\)\(^{\oplus 2}\)