Space of modular forms of level 26, weight 3, and Character 26.f

• Label: 26.3.f
• Level: $26$
• Weight: $3$
• Character orbit: 26.f
• Rep. character: $\chi_{26}(7,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $10$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	26.f (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(10\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(26, [\chi])\).

	Total	New	Old
Modular forms	36	12	24
Cusp forms	20	12	8
Eisenstein series	16	0	16

Trace form

12 * q - 2 * q^2 + 6 * q^5 - 24 * q^7 - 8 * q^8 - 30 * q^9 - 30 * q^10 - 24 * q^11 + 24 * q^13 + 16 * q^14 + 72 * q^15 + 24 * q^16 + 36 * q^17 + 108 * q^18 - 12 * q^19 + 12 * q^20 - 60 * q^21 - 24 * q^22 - 24 * q^23 + 26 * q^26 + 72 * q^27 - 48 * q^28 - 60 * q^29 - 192 * q^30 - 96 * q^31 + 8 * q^32 + 12 * q^33 - 84 * q^34 - 36 * q^35 - 48 * q^36 - 66 * q^37 - 24 * q^40 + 132 * q^41 + 144 * q^42 + 12 * q^43 + 120 * q^44 + 276 * q^45 + 144 * q^46 + 192 * q^47 + 300 * q^49 + 232 * q^50 + 72 * q^52 - 300 * q^53 - 360 * q^54 - 156 * q^55 - 96 * q^56 - 396 * q^57 - 66 * q^58 + 24 * q^59 - 96 * q^60 + 114 * q^61 - 72 * q^62 - 192 * q^63 - 420 * q^65 + 96 * q^66 + 12 * q^67 + 36 * q^68 + 132 * q^69 + 240 * q^70 - 132 * q^71 + 156 * q^72 + 30 * q^73 - 70 * q^74 + 120 * q^75 + 24 * q^76 + 216 * q^78 + 96 * q^79 + 24 * q^80 - 30 * q^81 - 330 * q^82 - 48 * q^83 - 168 * q^84 - 66 * q^85 - 24 * q^86 + 264 * q^87 + 234 * q^89 + 336 * q^91 - 48 * q^92 + 492 * q^93 + 72 * q^94 + 672 * q^95 + 222 * q^97 - 158 * q^98 + 144 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(26, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
26.3.f.a	$26$	$3$	26.f	13.f	$12$	$4$	$1$	$0.708$	\(\Q(\zeta_{12})\)	None		✓			26.3.f.a	$2$	$0$	\(2\)	\(0\)	\(0\)	\(-22\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
26.3.f.b	$26$	$3$	26.f	13.f	$12$	$8$	$2$	$0.708$	8.0.\(\cdots\).1	None		✓	✓		26.3.f.b	$2$	$0$	\(-4\)	\(0\)	\(6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(26, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(26, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)