Space of modular forms of level 621, weight 2, and Character 621.s

• Label: 621.2.s
• Level: $621$
• Weight: $2$
• Character orbit: 621.s
• Rep. character: $\chi_{621}(17,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $440$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 621 = 3^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	621.s (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 207 \)
Character field:			\(\Q(\zeta_{66})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(621, [\chi])\).

	Total	New	Old
Modular forms	1560	520	1040
Cusp forms	1320	440	880
Eisenstein series	240	80	160

Trace form

440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(621, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
621.2.s.a	$621$	$2$	621.s	207.o	$66$	$440$	$22$	$4.959$		None			✓	✓	207.2.o.a	$4$	$0$	\(27\)	\(0\)	\(33\)	\(-11\)		$\mathrm{SU}(2)[C_{66}]$

Decomposition of \(S_{2}^{\mathrm{old}}(621, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(621, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)