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

• Label: 490.2.i
• Level: $490$
• Weight: $2$
• Character orbit: 490.i
• Rep. character: $\chi_{490}(79,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $40$
• Newform subspaces: $6$
• Sturm bound: $168$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
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	200	40	160
Cusp forms	136	40	96
Eisenstein series	64	0	64

Trace form

40 * q + 20 * q^4 - 2 * q^5 + 12 * q^6 + 14 * q^9 - 2 * q^10 + 10 * q^11 + 32 * q^15 - 20 * q^16 + 14 * q^19 - 4 * q^20 + 6 * q^24 - 14 * q^26 - 28 * q^29 - 6 * q^30 + 16 * q^31 - 16 * q^34 + 28 * q^36 - 12 * q^39 + 2 * q^40 - 10 * q^44 - 24 * q^45 - 24 * q^46 + 20 * q^51 + 18 * q^54 + 24 * q^55 + 4 * q^59 + 16 * q^60 - 6 * q^61 - 40 * q^64 + 30 * q^65 + 12 * q^69 + 16 * q^71 - 30 * q^74 - 24 * q^75 + 28 * q^76 - 16 * q^79 - 2 * q^80 + 20 * q^81 - 64 * q^85 + 18 * q^86 + 10 * q^89 - 60 * q^90 - 2 * q^94 - 28 * q^95 - 6 * q^96 - 60 * 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.i.a	$490$	$2$	490.i	35.j	$6$	$4$	$2$	$3.913$	\(\Q(\zeta_{12})\)	None					70.2.i.b	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}+\cdots)q^{5}+\cdots\)
490.2.i.b	$490$	$2$	490.i	35.j	$6$	$4$	$2$	$3.913$	\(\Q(\zeta_{12})\)	None					70.2.i.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
490.2.i.c	$490$	$2$	490.i	35.j	$6$	$8$	$4$	$3.913$	\(\Q(\zeta_{24})\)	None					70.2.c.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta_{4}-\beta_1)q^{2}+(-\beta_{6}-\beta_{5})q^{3}+\cdots\)
490.2.i.d	$490$	$2$	490.i	35.j	$6$	$8$	$4$	$3.913$	\(\Q(\zeta_{24})\)	None		✓			490.2.c.g	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
490.2.i.e	$490$	$2$	490.i	35.j	$6$	$8$	$4$	$3.913$	\(\Q(\zeta_{24})\)	None		✓			490.2.c.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{24}^{2}q^{2}+(-\zeta_{24}+\zeta_{24}^{7})q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)
490.2.i.f	$490$	$2$	490.i	35.j	$6$	$8$	$4$	$3.913$	\(\Q(\zeta_{24})\)	None					70.2.c.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta_{4}-\beta_1)q^{2}+(-\beta_{6}-\beta_{5})q^{3}+\cdots\)

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

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