Space of modular forms of level 497, weight 2, and Character 497.v

• Label: 497.2.v
• Level: $497$
• Weight: $2$
• Character orbit: 497.v
• Rep. character: $\chi_{497}(8,\cdot)$
• Character field: $\Q(\zeta_{35})$
• Dimension: $864$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$497 = 7 \cdot 71$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	497.v (of order $35$ and degree $24$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$71$
Character field:			$\Q(\zeta_{35})$
Newform subspaces:			$2$
Sturm bound:			$96$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(497, [\chi])$.

	Total	New	Old
Modular forms	1200	864	336
Cusp forms	1104	864	240
Eisenstein series	96	0	96

Trace form

864 * q - 3 * q^2 - 10 * q^3 + 33 * q^4 + 4 * q^5 - 18 * q^6 + 2 * q^7 + 13 * q^8 + 20 * q^9 + 16 * q^10 + 6 * q^11 - 26 * q^12 + 8 * q^13 - 22 * q^14 - 38 * q^15 - 29 * q^16 - 6 * q^17 - 53 * q^18 + 12 * q^19 - 120 * q^20 + 8 * q^21 + 15 * q^22 - 40 * q^23 + 38 * q^24 - 188 * q^25 - 50 * q^26 - 94 * q^27 - 11 * q^28 - 22 * q^29 - 52 * q^30 - 72 * q^31 + 20 * q^32 - 38 * q^33 + 20 * q^34 + 8 * q^35 - 36 * q^36 + 20 * q^37 + 42 * q^38 - 212 * q^39 - 8 * q^40 - 74 * q^41 + 4 * q^42 - 90 * q^43 - 17 * q^44 - 128 * q^45 - 154 * q^46 + 8 * q^47 - 202 * q^48 + 36 * q^49 + 38 * q^50 - 52 * q^51 - 32 * q^52 + 54 * q^53 + 4 * q^55 + 76 * q^56 - 112 * q^57 + 15 * q^58 - 12 * q^59 - 254 * q^60 + 38 * q^61 + 150 * q^62 + 98 * q^63 + 15 * q^64 + 120 * q^65 - 90 * q^66 - 8 * q^67 + 80 * q^68 + 138 * q^69 + 104 * q^70 + 2 * q^71 + 306 * q^72 - 92 * q^73 - 9 * q^74 + 144 * q^75 - 64 * q^76 + 88 * q^77 - 28 * q^78 + 52 * q^79 - 162 * q^80 - 20 * q^81 + 192 * q^82 + 64 * q^83 + 212 * q^84 - 20 * q^85 + 44 * q^86 - 18 * q^87 - 237 * q^88 - 94 * q^89 - 92 * q^90 - 68 * q^91 + 44 * q^92 - 64 * q^93 - 140 * q^94 - 96 * q^95 - 138 * q^96 - 84 * q^97 + 2 * q^98 - 50 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(497, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
497.2.v.a	$497$	$2$	497.v	71.g	$35$	$408$	$17$	$3.969$		None		✓			497.2.v.a	$2$	$0$	$-2$	$-4$	$26$	$-17$		$\mathrm{SU}(2)[C_{35}]$
497.2.v.b	$497$	$2$	497.v	71.g	$35$	$456$	$19$	$3.969$		None		✓	✓		497.2.v.b	$2$	$0$	$-1$	$-6$	$-22$	$19$		$\mathrm{SU}(2)[C_{35}]$

Decomposition of $S_{2}^{\mathrm{old}}(497, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(497, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(71, [\chi])$$^{\oplus 2}$