Space of modular forms of level 269, weight 8, and trivial character

• Label: 269.8.a
• Level: $269$
• Weight: $8$
• Character orbit: 269.a
• Rep. character: $\chi_{269}(1,\cdot)$
• Character field: $\Q$
• Dimension: $157$
• Newform subspaces: $2$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 269 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	269.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(269))\).

	Total	New	Old
Modular forms	159	157	2
Cusp forms	157	157	0
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(269\)	Dim
\(+\)	\(84\)
\(-\)	\(73\)

Trace form

157 * q + 6 * q^2 - 28 * q^3 + 10046 * q^4 + 2 * q^5 - 580 * q^6 - 1350 * q^7 - 1320 * q^8 + 118117 * q^9 - 5618 * q^10 + 6640 * q^11 + 9960 * q^12 + 7010 * q^13 + 9096 * q^14 - 29594 * q^15 + 610998 * q^16 - 41154 * q^17 + 6576 * q^18 - 25504 * q^19 + 10612 * q^20 + 67596 * q^21 + 87596 * q^22 + 39938 * q^23 - 60318 * q^24 + 2549423 * q^25 + 52736 * q^26 - 54778 * q^27 - 674848 * q^28 - 173192 * q^29 + 442098 * q^30 - 57338 * q^31 + 77586 * q^32 - 83660 * q^33 + 213932 * q^34 - 313354 * q^35 + 7804162 * q^36 + 277840 * q^37 + 45404 * q^38 + 90766 * q^39 - 643812 * q^40 + 631596 * q^41 - 1811082 * q^42 + 68430 * q^43 + 288014 * q^44 - 621306 * q^45 + 1373776 * q^46 + 231918 * q^47 + 228836 * q^48 + 19766657 * q^49 + 1676372 * q^50 + 878004 * q^51 + 5979004 * q^52 - 2820262 * q^53 - 1508318 * q^54 + 3210368 * q^55 + 2224988 * q^56 + 1505440 * q^57 - 1495546 * q^58 + 1990276 * q^59 - 4824018 * q^60 - 1784188 * q^61 - 12544 * q^62 - 6625512 * q^63 + 38544048 * q^64 - 7113866 * q^65 + 2597848 * q^66 + 801822 * q^67 - 4720592 * q^68 - 2716774 * q^69 - 26916744 * q^70 - 8200354 * q^71 - 16169526 * q^72 - 1976168 * q^73 - 3491164 * q^74 - 3272344 * q^75 - 4731536 * q^76 - 2402328 * q^77 - 21591786 * q^78 + 7819154 * q^79 - 4436666 * q^80 + 78595349 * q^81 + 1648102 * q^82 + 3208056 * q^83 + 11160200 * q^84 + 32892422 * q^85 - 8745808 * q^86 + 6501602 * q^87 - 2511680 * q^88 - 13702138 * q^89 - 11874584 * q^90 - 17362162 * q^91 + 38659678 * q^92 + 13961908 * q^93 + 20068474 * q^94 - 48864028 * q^95 - 81613836 * q^96 + 1087728 * q^97 + 12166802 * q^98 + 6370756 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(269))\) 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					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		269
269.8.a.a	$269$	$8$	269.a	1.a	$1$	$73$	$73$	$84.032$		None	✓	✓	✓	✓	269.8.a.a	$1$	$1$	\(-17\)	\(-203\)	\(-499\)	\(-5477\)		$-$	$-$		$\mathrm{SU}(2)$
269.8.a.b	$269$	$8$	269.a	1.a	$1$	$84$	$84$	$84.032$		None	✓	✓	✓	✓	269.8.a.b	$1$	$0$	\(23\)	\(175\)	\(501\)	\(4127\)		$+$	$+$		$\mathrm{SU}(2)$