Space of modular forms of level 26, weight 8, and Character 26.c

• Label: 26.8.c
• Level: $26$
• Weight: $8$
• Character orbit: 26.c
• Rep. character: $\chi_{26}(3,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $28$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(28\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(26, [\chi])\).

	Total	New	Old
Modular forms	54	14	40
Cusp forms	46	14	32
Eisenstein series	8	0	8

Trace form

14 * q + 8 * q^2 - 448 * q^4 - 110 * q^5 + 612 * q^7 - 1024 * q^8 - 3335 * q^9 + 4888 * q^10 - 11620 * q^11 - 33319 * q^13 - 27328 * q^14 + 3104 * q^15 - 28672 * q^16 + 21579 * q^17 - 113488 * q^18 - 97536 * q^19 + 3520 * q^20 + 345416 * q^21 + 25312 * q^22 + 2572 * q^23 + 339264 * q^25 - 211640 * q^26 + 133920 * q^27 + 39168 * q^28 + 96931 * q^29 - 223616 * q^30 + 51592 * q^31 + 32768 * q^32 + 656540 * q^33 + 560848 * q^34 - 368636 * q^35 - 213440 * q^36 - 95601 * q^37 - 1635840 * q^38 + 1046136 * q^39 - 625664 * q^40 + 855255 * q^41 + 75520 * q^42 - 449256 * q^43 + 1487360 * q^44 - 1501253 * q^45 + 554784 * q^46 - 2560912 * q^47 - 228915 * q^49 + 32992 * q^50 - 8250592 * q^51 + 1329536 * q^52 - 1974654 * q^53 + 1164672 * q^54 - 173468 * q^55 + 874496 * q^56 + 9514040 * q^57 - 714792 * q^58 + 3055012 * q^59 - 397312 * q^60 - 946005 * q^61 + 4772192 * q^62 - 5388564 * q^63 + 3670016 * q^64 - 9946885 * q^65 - 2868224 * q^66 + 7282252 * q^67 + 1381056 * q^68 + 9273828 * q^69 + 10427584 * q^70 - 3528832 * q^71 + 3631616 * q^72 + 6328546 * q^73 - 610632 * q^74 + 27970672 * q^75 - 6242304 * q^76 - 44793976 * q^77 - 5915520 * q^78 - 12571016 * q^79 + 225280 * q^80 + 9167137 * q^81 + 5515768 * q^82 + 23507040 * q^83 - 11053312 * q^84 + 36700549 * q^85 - 11028352 * q^86 - 11990280 * q^87 + 1619968 * q^88 - 8841162 * q^89 - 49688560 * q^90 - 7985016 * q^91 - 329216 * q^92 + 2034720 * q^93 + 1056448 * q^94 - 13012128 * q^95 - 9478914 * q^97 + 9653448 * q^98 - 23827928 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(26, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
26.8.c.a	$26$	$8$	26.c	13.c	$3$	$6$	$3$	$8.122$	\(\mathbb{Q}[x]/(x^{6} + \cdots)\)	None		✓			26.8.c.a	$2$	$0$	\(-24\)	\(0\)	\(-666\)	\(1160\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-8-8\beta _{3})q^{2}-\beta _{1}q^{3}+2^{6}\beta _{3}q^{4}+\cdots\)
26.8.c.b	$26$	$8$	26.c	13.c	$3$	$8$	$4$	$8.122$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓		26.8.c.b	$2$	$0$	\(32\)	\(0\)	\(556\)	\(-548\)	$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{3}]$	\(q-8\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{6}-2^{6}\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(26, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(26, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)