Space of modular forms of level 340, weight 2, and Character 340.l

• Label: 340.2.l
• Level: $340$
• Weight: $2$
• Character orbit: 340.l
• Rep. character: $\chi_{340}(103,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $108$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 340 = 2^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	340.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 20 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(108\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(340, [\chi])\).

	Total	New	Old
Modular forms	116	96	20
Cusp forms	100	96	4
Eisenstein series	16	0	16

Trace form

96 * q - 12 * q^8 - 16 * q^10 - 16 * q^12 + 28 * q^18 + 20 * q^20 - 16 * q^21 + 4 * q^22 - 32 * q^26 + 12 * q^28 - 4 * q^30 + 16 * q^33 - 32 * q^36 - 40 * q^38 + 4 * q^40 + 16 * q^41 + 20 * q^42 - 48 * q^46 + 28 * q^48 + 4 * q^50 + 20 * q^52 - 48 * q^53 + 8 * q^56 - 32 * q^57 + 48 * q^58 - 60 * q^60 - 56 * q^62 - 32 * q^65 + 64 * q^66 + 16 * q^70 - 40 * q^72 - 16 * q^73 + 8 * q^76 + 28 * q^78 - 36 * q^80 - 16 * q^81 - 84 * q^82 + 8 * q^86 - 16 * q^88 + 60 * q^90 + 16 * q^92 + 48 * q^93 - 96 * q^96 - 80 * q^97 - 36 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(340, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
340.2.l.a	$340$	$2$	340.l	20.e	$4$	$8$	$4$	$2.715$	8.0.18939904.2	None		✓			340.2.l.a	$4$	$0$	\(4\)	\(0\)	\(-16\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1-\beta _{2}+\beta _{5}-\beta _{7})q^{2}+(-1-2\beta _{3}+\cdots)q^{3}+\cdots\)
340.2.l.b	$340$	$2$	340.l	20.e	$4$	$88$	$44$	$2.715$		None		✓	✓		340.2.l.b	$4$	$0$	\(-4\)	\(0\)	\(16\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(340, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(340, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)