Space of modular forms of level 260, weight 2, and Character 260.z

• Label: 260.2.z
• Level: $260$
• Weight: $2$
• Character orbit: 260.z
• Rep. character: $\chi_{260}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.z (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(84\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(260, [\chi])\).

	Total	New	Old
Modular forms	96	16	80
Cusp forms	72	16	56
Eisenstein series	24	0	24

Trace form

16 * q + 10 * q^9 - 6 * q^11 + 6 * q^15 - 18 * q^19 - 14 * q^25 + 12 * q^29 + 18 * q^39 - 48 * q^41 + 45 * q^45 - 6 * q^49 + 44 * q^51 + 2 * q^55 - 30 * q^59 - 28 * q^61 - 15 * q^65 - 34 * q^69 - 18 * q^71 - 42 * q^75 - 16 * q^79 - 44 * q^81 - 45 * q^85 + 30 * q^89 - 10 * q^91

Decomposition of \(S_{2}^{\mathrm{new}}(260, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
260.2.z.a	$260$	$2$	260.z	65.l	$6$	$16$	$8$	$2.076$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓	✓	260.2.z.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{3}+\beta _{14}q^{5}-\beta _{8}q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(260, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(260, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)