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

• Label: 340.2.c
• Level: $340$
• Weight: $2$
• Character orbit: 340.c
• Rep. character: $\chi_{340}(101,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 340 = 2^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	340.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	60	6	54
Cusp forms	48	6	42
Eisenstein series	12	0	12

Trace form

6 * q - 14 * q^9 + 4 * q^15 - 2 * q^17 + 16 * q^19 - 24 * q^21 - 6 * q^25 - 12 * q^33 - 8 * q^35 - 16 * q^43 + 32 * q^47 + 2 * q^49 + 4 * q^51 + 44 * q^53 + 16 * q^55 - 8 * q^59 - 8 * q^67 + 32 * q^69 + 20 * q^77 + 38 * q^81 + 16 * q^83 - 4 * q^85 - 64 * q^87 - 36 * q^89 - 52 * q^93

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.c.a	$340$	$2$	340.c	17.b	$2$	$6$	$6$	$2.715$	6.0.37161216.1	None		✓	✓	✓	340.2.c.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{4})q^{3}+\beta _{4}q^{5}+(\beta _{1}+\beta _{4})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(340, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)