Space of modular forms of level 26, weight 10, and Character 26.c

• Label: 26.10.c
• Level: $26$
• Weight: $10$
• Character orbit: 26.c
• Rep. character: $\chi_{26}(3,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $22$
• Newform subspaces: $2$
• Sturm bound: $35$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	26.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(35\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(26, [\chi])\).

	Total	New	Old
Modular forms	66	22	44
Cusp forms	58	22	36
Eisenstein series	8	0	8

Trace form

22 * q - 16 * q^2 - 162 * q^3 - 2816 * q^4 + 1558 * q^5 + 2850 * q^7 + 8192 * q^8 - 83597 * q^9 - 41712 * q^10 + 39326 * q^11 + 82944 * q^12 + 218387 * q^13 + 121472 * q^14 + 360776 * q^15 - 720896 * q^16 + 303 * q^17 + 1792928 * q^18 - 354718 * q^19 - 199424 * q^20 + 2116244 * q^21 - 1077568 * q^22 + 948802 * q^23 + 4884684 * q^25 - 2625872 * q^26 + 3245652 * q^27 + 729600 * q^28 - 13963961 * q^29 + 3660544 * q^30 + 26782816 * q^31 - 1048576 * q^32 - 25872262 * q^33 - 11098016 * q^34 - 22104464 * q^35 - 21400832 * q^36 + 21602195 * q^37 + 9280512 * q^38 + 15239670 * q^39 + 21356544 * q^40 - 274845 * q^41 - 55290368 * q^42 - 80271378 * q^43 - 20134912 * q^44 + 32348653 * q^45 + 37451840 * q^46 + 174846344 * q^47 - 10616832 * q^48 - 97855497 * q^49 - 46924736 * q^50 + 97279532 * q^51 + 31096832 * q^52 - 146214090 * q^53 + 55501056 * q^54 + 292255248 * q^55 - 15548416 * q^56 - 434760508 * q^57 - 122216176 * q^58 + 18272290 * q^59 - 184717312 * q^60 + 319834719 * q^61 - 119661376 * q^62 + 116485392 * q^63 + 369098752 * q^64 + 75817181 * q^65 + 849000448 * q^66 - 320197838 * q^67 + 77568 * q^68 - 282159582 * q^69 - 568530048 * q^70 + 238656386 * q^71 - 229494784 * q^72 + 781839782 * q^73 + 157099728 * q^74 - 999434810 * q^75 - 90807808 * q^76 + 2326837844 * q^77 + 197674752 * q^78 - 163472152 * q^79 - 51052544 * q^80 - 856730123 * q^81 + 53212816 * q^82 - 3041665536 * q^83 - 270879232 * q^84 - 2913176369 * q^85 + 692734208 * q^86 + 1111006674 * q^87 - 275857408 * q^88 + 1257526860 * q^89 + 2226819680 * q^90 + 571941238 * q^91 - 485786624 * q^92 - 3106387752 * q^93 - 782253184 * q^94 + 105002424 * q^95 + 3307136932 * q^97 - 3635475600 * q^98 - 3704648192 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(26, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
26.10.c.a	$26$	$10$	26.c	13.c	$3$	$10$	$5$	$13.391$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓			26.10.c.a	$2$	$0$	\(80\)	\(-81\)	\(-1828\)	\(3323\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2^{4}-2^{4}\beta _{2})q^{2}+(-2^{4}-\beta _{1}+2^{4}\beta _{2}+\cdots)q^{3}+\cdots\)
26.10.c.b	$26$	$10$	26.c	13.c	$3$	$12$	$6$	$13.391$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		26.10.c.b	$2$	$0$	\(-96\)	\(-81\)	\(3386\)	\(-473\)	$2^{12}\cdot 3^{7}\cdot 13^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-2^{4}+2^{4}\beta _{1})q^{2}+(-14+14\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(26, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(26, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)