Space of modular forms of level 3420, weight 2, and Character 3420.dg

• Label: 3420.2.dg
• Level: $3420$
• Weight: $2$
• Character orbit: 3420.dg
• Rep. character: $\chi_{3420}(521,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $3$
• Sturm bound: $1440$
• Trace bound: $17$

Defining parameters

Level:	\( N \)	\(=\)	\( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3420.dg (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(1440\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3420, [\chi])\).

	Total	New	Old
Modular forms	1488	48	1440
Cusp forms	1392	48	1344
Eisenstein series	96	0	96

Trace form

\( 48 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3420, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3420.2.dg.a	$3420$	$2$	3420.dg	57.f	$6$	$8$	$4$	$27.309$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{5}+(-1-\zeta_{24}+2\zeta_{24}^{2}+\cdots)q^{7}+\cdots\)
3420.2.dg.b	$3420$	$2$	3420.dg	57.f	$6$	$8$	$4$	$27.309$	\(\Q(\zeta_{24})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{24}^{2}+\zeta_{24}^{6})q^{5}+(-1-\zeta_{24}+\cdots)q^{7}+\cdots\)
3420.2.dg.c	$3420$	$2$	3420.dg	57.f	$6$	$32$	$16$	$27.309$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3420, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3420, [\chi]) \cong \)