Space of modular forms of level 2349, weight 1, and Character 2349.h

• Label: 2349.1.h
• Level: $2349$
• Weight: $1$
• Character orbit: 2349.h
• Rep. character: $\chi_{2349}(782,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $270$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 2349 = 3^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2349.h (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 261 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(270\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2349, [\chi])\).

	Total	New	Old
Modular forms	40	20	20
Cusp forms	16	16	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	16	0	0	0

Trace form

\( 16 q - 6 q^{4} + 2 q^{7} + 2 q^{13} - 4 q^{16} + 4 q^{22} - 8 q^{25} - 12 q^{28} + 4 q^{34} - 6 q^{49} + 6 q^{52} + 2 q^{58} + 4 q^{64} + 2 q^{67} - 8 q^{82} + 8 q^{88} - 8 q^{91} + 4 q^{94}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2349, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2349.1.h.a	$2349$	$1$	2349.h	261.h	$6$	$2$	$1$	$1.172$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-87}) \)	None					87.1.d.a	$4$	$0$	\(-1\)	\(0\)	\(0\)	\(1\)	$1$		\(q-\zeta_{6}q^{2}+\zeta_{6}q^{7}-q^{8}-\zeta_{6}q^{11}-\zeta_{6}^{2}q^{13}+\cdots\)
2349.1.h.b	$2349$	$1$	2349.h	261.h	$6$	$2$	$1$	$1.172$	\(\Q(\sqrt{-3}) \)	$D_{3}$	\(\Q(\sqrt{-87}) \)	None					87.1.d.a	$4$	$0$	\(1\)	\(0\)	\(0\)	\(1\)	$1$		\(q+\zeta_{6}q^{2}+\zeta_{6}q^{7}+q^{8}+\zeta_{6}q^{11}-\zeta_{6}^{2}q^{13}+\cdots\)
2349.1.h.c	$2349$	$1$	2349.h	261.h	$6$	$6$	$3$	$1.172$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-87}) \)	None					783.1.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$		\(q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots\)
2349.1.h.d	$2349$	$1$	2349.h	261.h	$6$	$6$	$3$	$1.172$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-87}) \)	None					783.1.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3$		\(q+(\zeta_{18}-\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots\)