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

• Label: 340.2.s
• Level: $340$
• Weight: $2$
• Character orbit: 340.s
• Rep. character: $\chi_{340}(183,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $100$
• Newform subspaces: $3$
• Sturm bound: $108$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 340 = 2^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	340.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 340 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(108\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

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

Trace form

100 * q - 6 * q^5 + 84 * q^9 - 6 * q^10 - 16 * q^12 - 8 * q^13 - 16 * q^14 - 16 * q^16 - 14 * q^17 - 12 * q^18 + 6 * q^20 - 16 * q^21 - 12 * q^22 - 8 * q^24 - 52 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 4 * q^34 + 12 * q^37 + 4 * q^38 + 6 * q^40 - 8 * q^41 - 16 * q^42 + 8 * q^44 - 46 * q^45 - 24 * q^46 + 52 * q^49 - 24 * q^50 + 12 * q^52 - 4 * q^54 - 12 * q^56 - 16 * q^58 - 32 * q^60 + 24 * q^61 + 40 * q^68 - 28 * q^70 - 16 * q^72 - 8 * q^74 - 56 * q^77 + 20 * q^78 + 14 * q^80 + 20 * q^81 + 44 * q^82 - 24 * q^85 + 8 * q^86 + 10 * q^90 - 24 * q^93 + 112 * q^94 + 40 * q^96 + 12 * q^97 + 16 * 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.s.a	$340$	$2$	340.s	340.s	$4$	$2$	$1$	$2.715$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			340.2.i.b	$4$	$1$	\(-2\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-i-1)q^{2}+2 i q^{4}+(2 i-1)q^{5}+\cdots\)
340.2.s.b	$340$	$2$	340.s	340.s	$4$	$2$	$1$	$2.715$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)		✓			340.2.i.a	$4$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-i-1)q^{2}+2 i q^{4}+(i+2)q^{5}+\cdots\)
340.2.s.c	$340$	$2$	340.s	340.s	$4$	$96$	$48$	$2.715$		None		✓	✓		340.2.i.c	$4$	$0$	\(4\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$