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

• Label: 261.2.q
• Level: $261$
• Weight: $2$
• Character orbit: 261.q
• Rep. character: $\chi_{261}(7,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $336$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.q (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 261 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	384	384	0
Cusp forms	336	336	0
Eisenstein series	48	48	0

Trace form

336 * q - 5 * q^2 - 10 * q^3 + 21 * q^4 - 9 * q^5 - 40 * q^6 - 5 * q^7 + 2 * q^8 - 6 * q^9 - 28 * q^10 - q^11 - 22 * q^12 - 5 * q^13 - 9 * q^14 - 26 * q^15 + 21 * q^16 - 60 * q^17 - 90 * q^18 - 20 * q^19 - 15 * q^20 - 2 * q^21 - 13 * q^22 - 32 * q^23 + 44 * q^24 + 15 * q^25 - 4 * q^26 - 43 * q^27 - 72 * q^28 - q^29 - 8 * q^30 - 5 * q^31 + 7 * q^32 - 37 * q^33 - 15 * q^34 + 16 * q^35 - 104 * q^36 - 20 * q^37 + 63 * q^38 + 38 * q^39 + 5 * q^40 - 20 * q^41 + 11 * q^42 - 5 * q^43 - 8 * q^44 + 30 * q^45 - 80 * q^46 + 5 * q^47 + 12 * q^48 - 19 * q^49 - 3 * q^50 - 62 * q^51 + q^52 - 4 * q^53 + 26 * q^54 - 100 * q^55 - 5 * q^56 - 50 * q^57 - 7 * q^58 + 154 * q^59 + 23 * q^60 + 7 * q^61 - 4 * q^62 - 144 * q^63 + 18 * q^64 - 65 * q^65 + 44 * q^66 - 5 * q^67 - 9 * q^68 + 22 * q^69 - 14 * q^70 + 18 * q^71 + 37 * q^72 - 20 * q^73 - 77 * q^74 + 16 * q^75 - 5 * q^76 + 39 * q^77 + 52 * q^78 - 5 * q^79 - 104 * q^80 + 54 * q^81 + 12 * q^82 - 23 * q^83 + 175 * q^84 - 42 * q^85 + 128 * q^86 + 42 * q^87 - 8 * q^88 + 34 * q^89 + 222 * q^90 + 12 * q^91 - 115 * q^92 + 64 * q^93 - 25 * q^94 + 89 * q^95 - 49 * q^96 + 55 * q^97 - 88 * q^98 + 196 * q^99

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.q.a	$261$	$2$	261.q	261.q	$21$	$336$	$28$	$2.084$		None		✓	✓	✓	261.2.q.a	$4$	$0$	\(-5\)	\(-10\)	\(-9\)	\(-5\)		$\mathrm{SU}(2)[C_{21}]$