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

• Label: 340.2.bd
• Level: $340$
• Weight: $2$
• Character orbit: 340.bd
• Rep. character: $\chi_{340}(57,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $72$
• 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.bd (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(\zeta_{16})\)
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	480	72	408
Cusp forms	384	72	312
Eisenstein series	96	0	96

Trace form

72 * q + 24 * q^15 + 8 * q^25 - 48 * q^27 - 32 * q^31 + 16 * q^33 + 32 * q^37 - 32 * q^39 - 40 * q^41 + 80 * q^47 - 40 * q^53 + 16 * q^55 + 8 * q^57 + 112 * q^59 - 48 * q^63 - 32 * q^67 - 16 * q^71 + 8 * q^73 - 88 * q^75 - 16 * q^77 - 64 * q^79 - 48 * q^81 - 40 * q^83 - 40 * q^85 - 8 * q^87 - 48 * q^91 - 120 * q^93 - 48 * q^95 - 80 * q^97 + 96 * q^99

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.bd.a	$340$	$2$	340.bd	85.o	$16$	$72$	$9$	$2.715$		None		✓	✓	✓	340.2.bd.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

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

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