Space of modular forms of level 3420, weight 1, and Character 3420.h

• Label: 3420.1.h
• Level: $3420$
• Weight: $1$
• Character orbit: 3420.h
• Rep. character: $\chi_{3420}(2089,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $720$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3420.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(720\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3420, [\chi])\).

	Total	New	Old
Modular forms	78	6	72
Cusp forms	54	6	48
Eisenstein series	24	0	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q + q^{5} - 2 q^{11} - 2 q^{19} + q^{25} + 3 q^{35} - 12 q^{49} + 5 q^{55} - 2 q^{61} + q^{85} + q^{95}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3420, [\chi])\) 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
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3420.1.h.a	$3420$	$1$	3420.h	95.d	$2$	$2$	$2$	$1.707$	\(\Q(\sqrt{-3}) \)	$D_{6}$	\(\Q(\sqrt{-19}) \)	None					380.1.g.a	$4$	$0$	\(0\)	\(0\)	\(1\)	\(0\)	$1$		\(q-\zeta_{6}^{2}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{11}+(\zeta_{6}+\cdots)q^{17}+\cdots\)
3420.1.h.b	$3420$	$1$	3420.h	95.d	$2$	$4$	$4$	$1.707$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-19}) \)	None		✓	✓		3420.1.h.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{5}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{7}+(-\zeta_{12}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3420, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3420, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(855, [\chi])\)\(^{\oplus 3}\)