Space of modular forms of level 2303, weight 1, and Character 2303.d

• Label: 2303.1.d
• Level: $2303$
• Weight: $1$
• Character orbit: 2303.d
• Rep. character: $\chi_{2303}(2255,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $5$
• Sturm bound: $224$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2303.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 47 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(224\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2303, [\chi])\).

	Total	New	Old
Modular forms	26	17	9
Cusp forms	18	12	6
Eisenstein series	8	5	3

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q - q^{2} + q^{3} + 11 q^{4} + 2 q^{6} - 2 q^{8} + 11 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2303, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2303.1.d.a	$2303$	$1$	2303.d	47.b	$2$	$1$	$1$	$1.149$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-47}) \)	None	✓				329.1.f.a	$2$	$0$	\(-1\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-q^{2}-2q^{3}+2q^{6}+q^{8}+3q^{9}-q^{16}+\cdots\)
2303.1.d.b	$2303$	$1$	2303.d	47.b	$2$	$1$	$1$	$1.149$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-47}) \)	None	✓				329.1.f.a	$2$	$0$	\(-1\)	\(2\)	\(0\)	\(0\)	$1$		\(q-q^{2}+2q^{3}-2q^{6}+q^{8}+3q^{9}-q^{16}+\cdots\)
2303.1.d.c	$2303$	$1$	2303.d	47.b	$2$	$2$	$2$	$1.149$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-47}) \)	None	✓				47.1.b.a	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}+(1-\beta )q^{3}+\beta q^{4}+q^{6}-q^{8}+\cdots\)
2303.1.d.d	$2303$	$1$	2303.d	47.b	$2$	$4$	$4$	$1.149$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-47}) \)	None	✓				329.1.f.b	$2$	$0$	\(1\)	\(-2\)	\(0\)	\(0\)	$1$		\(q+(1-\beta _{1}+\beta _{3})q^{2}+\beta _{3}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
2303.1.d.e	$2303$	$1$	2303.d	47.b	$2$	$4$	$4$	$1.149$	\(\Q(\zeta_{15})^+\)	$D_{15}$	\(\Q(\sqrt{-47}) \)	None	✓				329.1.f.b	$2$	$0$	\(1\)	\(2\)	\(0\)	\(0\)	$1$		\(q+(1-\beta _{1}+\beta _{3})q^{2}-\beta _{3}q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2303, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2303, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(47, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(329, [\chi])\)\(^{\oplus 2}\)