Space of modular forms of level 261, weight 2, and Character 261.k

• Label: 261.2.k
• Level: $261$
• Weight: $2$
• Character orbit: 261.k
• Rep. character: $\chi_{261}(82,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $66$
• Newform subspaces: $4$
• Sturm bound: $60$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.k (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(60\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(261, [\chi])\).

	Total	New	Old
Modular forms	204	78	126
Cusp forms	156	66	90
Eisenstein series	48	12	36

Trace form

66 * q + 8 * q^2 - 12 * q^4 + 7 * q^5 - 7 * q^7 + 25 * q^8 - 3 * q^10 - 9 * q^11 + 11 * q^13 + 3 * q^14 - 14 * q^16 + 20 * q^17 - 7 * q^19 - 52 * q^20 - 22 * q^22 + 21 * q^23 + 14 * q^25 - 6 * q^26 - 4 * q^28 - 4 * q^29 - 27 * q^31 - 51 * q^32 - 64 * q^34 - 39 * q^35 - 25 * q^37 + 50 * q^38 - 12 * q^40 + 24 * q^41 + 9 * q^43 + 42 * q^44 - 16 * q^46 - 35 * q^47 - 16 * q^49 - 17 * q^50 + 14 * q^52 - 7 * q^53 - 21 * q^55 - 45 * q^56 + 62 * q^58 + 68 * q^59 + 63 * q^61 - 151 * q^62 - 77 * q^64 - 33 * q^65 - 13 * q^67 - 18 * q^68 + 134 * q^70 - 39 * q^71 - 59 * q^73 + 88 * q^74 + 95 * q^76 - q^77 - 5 * q^79 + 178 * q^80 + 18 * q^82 - 9 * q^83 + 52 * q^85 + 40 * q^86 + 18 * q^88 + 71 * q^89 + 25 * q^91 + 110 * q^92 - 44 * q^94 + 75 * q^95 - 97 * q^97 - 39 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(261, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
261.2.k.a	$261$	$2$	261.k	29.d	$7$	$6$	$1$	$2.084$	\(\Q(\zeta_{14})\)	None					29.2.d.a	$2$	$0$	\(2\)	\(0\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(1-\zeta_{14}-\zeta_{14}^{3}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+\cdots\)
261.2.k.b	$261$	$2$	261.k	29.d	$7$	$18$	$3$	$2.084$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None					87.2.g.b	$2$	$0$	\(2\)	\(0\)	\(7\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+\beta _{3}q^{2}+(-\beta _{10}-\beta _{16})q^{4}+(-\beta _{6}+\cdots)q^{5}+\cdots\)
261.2.k.c	$261$	$2$	261.k	29.d	$7$	$18$	$3$	$2.084$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None					87.2.g.a	$2$	$0$	\(4\)	\(0\)	\(1\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(\beta _{3}-\beta _{9})q^{2}+(2\beta _{1}+\beta _{5}-\beta _{6}+2\beta _{12}+\cdots)q^{4}+\cdots\)
261.2.k.d	$261$	$2$	261.k	29.d	$7$	$24$	$4$	$2.084$		None		✓	✓		261.2.k.d	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{7}]$

Decomposition of \(S_{2}^{\mathrm{old}}(261, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(261, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 2}\)