Space of modular forms of level 3364, weight 1, and Character 3364.h

• Label: 3364.1.h
• Level: $3364$
• Weight: $1$
• Character orbit: 3364.h
• Rep. character: $\chi_{3364}(63,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $48$
• Newform subspaces: $5$
• Sturm bound: $435$
• Trace bound: $20$

Defining parameters

Level:	\( N \)	\(=\)	\( 3364 = 2^{2} \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3364.h (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 116 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(435\)
Trace bound:			\(20\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3364, [\chi])\).

	Total	New	Old
Modular forms	228	204	24
Cusp forms	48	48	0
Eisenstein series	180	156	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	48	0	0	0

Trace form

\( 48 q + 4 q^{4} + 2 q^{6} + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3364, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3364.1.h.a	$3364$	$1$	3364.h	116.h	$14$	$6$	$1$	$1.679$	\(\Q(\zeta_{14})\)	$D_{3}$	\(\Q(\sqrt{-29}) \)	None		$12$	$0$	\(-1\)	\(1\)	\(1\)	\(0\)	$1$		\(q+\zeta_{14}^{2}q^{2}+\zeta_{14}^{3}q^{3}+\zeta_{14}^{4}q^{4}+\cdots\)
3364.1.h.b	$3364$	$1$	3364.h	116.h	$14$	$6$	$1$	$1.679$	\(\Q(\zeta_{14})\)	$D_{3}$	\(\Q(\sqrt{-29}) \)	None		$12$	$0$	\(1\)	\(-1\)	\(1\)	\(0\)	$1$		\(q-\zeta_{14}^{2}q^{2}-\zeta_{14}^{3}q^{3}+\zeta_{14}^{4}q^{4}+\cdots\)
3364.1.h.c	$3364$	$1$	3364.h	116.h	$14$	$12$	$2$	$1.679$	\(\Q(\zeta_{28})\)	$D_{7}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$1$		\(q-\zeta_{28}^{11}q^{2}-\zeta_{28}^{8}q^{4}+(-1-\zeta_{28}^{8}+\cdots)q^{5}+\cdots\)
3364.1.h.d	$3364$	$1$	3364.h	116.h	$14$	$12$	$2$	$1.679$	\(\Q(\zeta_{28})\)	$D_{7}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q-\zeta_{28}^{11}q^{2}-\zeta_{28}^{8}q^{4}+(\zeta_{28}^{10}-\zeta_{28}^{12}+\cdots)q^{5}+\cdots\)
3364.1.h.e	$3364$	$1$	3364.h	116.h	$14$	$12$	$2$	$1.679$	\(\Q(\zeta_{28})\)	$D_{7}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q-\zeta_{28}^{11}q^{2}-\zeta_{28}^{8}q^{4}+(\zeta_{28}^{2}+\zeta_{28}^{6}+\cdots)q^{5}+\cdots\)