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

• Label: 490.2.c
• Level: $490$
• Weight: $2$
• Character orbit: 490.c
• Rep. character: $\chi_{490}(99,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $7$
• Sturm bound: $168$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(168\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(3\), \(11\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	100	20	80
Cusp forms	68	20	48
Eisenstein series	32	0	32

Trace form

20 * q - 20 * q^4 - 4 * q^5 - 8 * q^9 - 4 * q^10 - 4 * q^11 - 8 * q^15 + 20 * q^16 + 16 * q^19 + 4 * q^20 + 8 * q^26 + 4 * q^29 - 12 * q^30 - 16 * q^31 - 8 * q^34 + 8 * q^36 - 24 * q^39 + 4 * q^40 + 24 * q^41 + 4 * q^44 + 12 * q^45 - 12 * q^50 - 8 * q^51 + 24 * q^55 - 16 * q^59 + 8 * q^60 - 24 * q^61 - 20 * q^64 - 24 * q^65 + 48 * q^66 - 48 * q^69 + 32 * q^71 + 36 * q^74 - 16 * q^76 + 16 * q^79 - 4 * q^80 + 52 * q^81 - 20 * q^85 + 12 * q^86 - 40 * q^89 + 12 * q^90 - 16 * q^94 + 16 * q^95 - 12 * 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.c.a	$490$	$2$	490.c	5.b	$2$	$2$	$2$	$3.913$	\(\Q(\sqrt{-1}) \)	None					70.2.i.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(-i-2)q^{5}-i q^{8}+\cdots\)
490.2.c.b	$490$	$2$	490.c	5.b	$2$	$2$	$2$	$3.913$	\(\Q(\sqrt{-1}) \)	None					70.2.i.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-3 i q^{3}-q^{4}+(-2 i-1)q^{5}+\cdots\)
490.2.c.c	$490$	$2$	490.c	5.b	$2$	$2$	$2$	$3.913$	\(\Q(\sqrt{-1}) \)	None					70.2.i.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+3 i q^{3}-q^{4}+(2 i+1)q^{5}+\cdots\)
490.2.c.d	$490$	$2$	490.c	5.b	$2$	$2$	$2$	$3.913$	\(\Q(\sqrt{-1}) \)	None					70.2.i.b	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}+(i+2)q^{5}-i q^{8}+\cdots\)
490.2.c.e	$490$	$2$	490.c	5.b	$2$	$4$	$4$	$3.913$	\(\Q(i, \sqrt{6})\)	None					70.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
490.2.c.f	$490$	$2$	490.c	5.b	$2$	$4$	$4$	$3.913$	\(\Q(\zeta_{8})\)	None		✓			490.2.c.f	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{3})q^{3}-q^{4}+(\zeta_{8}+\cdots)q^{5}+\cdots\)
490.2.c.g	$490$	$2$	490.c	5.b	$2$	$4$	$4$	$3.913$	\(\Q(\zeta_{8})\)	None		✓			490.2.c.g	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(490, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)