Space of modular forms of level 490, weight 2, and Character 490.q

• Label: 490.2.q
• Level: $490$
• Weight: $2$
• Character orbit: 490.q
• Rep. character: $\chi_{490}(11,\cdot)$
• Character field: $\Q(\zeta_{21})$
• Dimension: $240$
• Newform subspaces: $4$
• Sturm bound: $168$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.q (of order \(21\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 49 \)
Character field:			\(\Q(\zeta_{21})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(168\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(490, [\chi])\).

	Total	New	Old
Modular forms	1056	240	816
Cusp forms	960	240	720
Eisenstein series	96	0	96

Trace form

240 * q + 20 * q^4 - 2 * q^5 + 10 * q^6 + 8 * q^7 + 40 * q^9 - 2 * q^10 + 2 * q^11 - 2 * q^14 + 20 * q^16 - 4 * q^17 + 8 * q^18 - 6 * q^19 + 4 * q^20 + 18 * q^21 - 8 * q^22 + 96 * q^23 + 2 * q^24 + 20 * q^25 + 24 * q^26 + 60 * q^27 - 4 * q^28 - 6 * q^29 + 2 * q^30 + 8 * q^31 - 24 * q^33 - 16 * q^34 + 8 * q^35 - 38 * q^36 - 4 * q^37 - 64 * q^38 + 52 * q^39 - 2 * q^40 - 72 * q^41 - 32 * q^42 + 24 * q^43 - 26 * q^44 - 4 * q^45 - 76 * q^46 - 8 * q^47 - 90 * q^49 - 92 * q^51 + 28 * q^52 - 92 * q^53 - 70 * q^54 - 16 * q^55 - 30 * q^56 - 8 * q^57 - 104 * q^58 - 38 * q^59 + 122 * q^61 - 8 * q^62 + 48 * q^63 - 40 * q^64 + 2 * q^65 + 8 * q^67 + 52 * q^68 + 92 * q^69 - 6 * q^70 - 64 * q^71 + 8 * q^72 + 56 * q^73 + 36 * q^74 + 12 * q^76 + 92 * q^77 - 32 * q^78 + 8 * q^79 + 12 * q^80 - 46 * q^81 - 16 * q^82 + 116 * q^83 - 8 * q^85 + 10 * q^86 - 200 * q^87 + 32 * q^88 - 30 * q^89 + 20 * q^90 - 30 * q^91 - 24 * q^92 + 20 * q^93 + 72 * q^94 + 8 * q^95 + 2 * q^96 - 176 * q^97 + 32 * q^98 + 108 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(490, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
490.2.q.a	$490$	$2$	490.q	49.g	$21$	$48$	$4$	$3.913$		None		✓			490.2.q.a	$2$	$0$	\(4\)	\(8\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{21}]$
490.2.q.b	$490$	$2$	490.q	49.g	$21$	$60$	$5$	$3.913$		None		✓			490.2.q.b	$2$	$0$	\(-5\)	\(-8\)	\(5\)	\(4\)		$\mathrm{SU}(2)[C_{21}]$
490.2.q.c	$490$	$2$	490.q	49.g	$21$	$60$	$5$	$3.913$		None		✓			490.2.q.c	$2$	$0$	\(-5\)	\(0\)	\(-5\)	\(1\)		$\mathrm{SU}(2)[C_{21}]$
490.2.q.d	$490$	$2$	490.q	49.g	$21$	$72$	$6$	$3.913$		None		✓	✓		490.2.q.d	$2$	$0$	\(6\)	\(0\)	\(-6\)	\(3\)		$\mathrm{SU}(2)[C_{21}]$

Decomposition of \(S_{2}^{\mathrm{old}}(490, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(490, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)