Space of modular forms of level 26, weight 4, and Character 26.c

• Label: 26.4.c
• Level: $26$
• Weight: $4$
• Character orbit: 26.c
• Rep. character: $\chi_{26}(3,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $14$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(14\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(26, [\chi])\).

	Total	New	Old
Modular forms	26	6	20
Cusp forms	18	6	12
Eisenstein series	8	0	8

Trace form

6 * q - 2 * q^2 + 6 * q^3 - 12 * q^4 - 10 * q^5 + 50 * q^7 + 16 * q^8 - 41 * q^9 + 18 * q^10 - 18 * q^11 - 48 * q^12 - 61 * q^13 - 160 * q^14 + 104 * q^15 - 48 * q^16 + 103 * q^17 + 308 * q^18 - 78 * q^19 + 20 * q^20 - 52 * q^21 + 16 * q^22 + 154 * q^23 - 476 * q^25 + 150 * q^26 - 396 * q^27 + 200 * q^28 + 211 * q^29 + 184 * q^30 + 352 * q^31 - 32 * q^32 + 806 * q^33 - 628 * q^34 - 256 * q^35 - 164 * q^36 + 279 * q^37 - 288 * q^38 - 1122 * q^39 - 144 * q^40 - 437 * q^41 + 112 * q^42 - 106 * q^43 + 144 * q^44 - 83 * q^45 - 440 * q^46 + 1224 * q^47 + 96 * q^48 - 117 * q^49 - 8 * q^50 + 1964 * q^51 + 464 * q^52 + 166 * q^53 + 936 * q^54 - 768 * q^55 + 320 * q^56 - 676 * q^57 + 370 * q^58 - 102 * q^59 - 832 * q^60 - 829 * q^61 - 768 * q^62 + 912 * q^63 + 384 * q^64 - 255 * q^65 - 2912 * q^66 - 710 * q^67 + 412 * q^68 - 186 * q^69 + 1104 * q^70 + 490 * q^71 - 616 * q^72 - 786 * q^73 + 2250 * q^74 - 1298 * q^75 - 312 * q^76 + 1164 * q^77 + 2424 * q^78 + 3048 * q^79 + 80 * q^80 + 253 * q^81 - 94 * q^82 - 4992 * q^83 + 104 * q^84 + 359 * q^85 - 1168 * q^86 - 1638 * q^87 + 64 * q^88 + 1912 * q^89 + 620 * q^90 - 1994 * q^91 - 1232 * q^92 - 2496 * q^93 + 328 * q^94 - 248 * q^95 + 976 * q^97 - 1506 * q^98 + 4384 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(26, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
26.4.c.a	$26$	$4$	26.c	13.c	$3$	$2$	$1$	$1.534$	\(\Q(\sqrt{-3}) \)	None		✓			26.4.c.a	$2$	$0$	\(2\)	\(3\)	\(4\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
26.4.c.b	$26$	$4$	26.c	13.c	$3$	$4$	$2$	$1.534$	\(\Q(\sqrt{-3}, \sqrt{217})\)	None		✓	✓		26.4.c.b	$2$	$0$	\(-4\)	\(3\)	\(-14\)	\(45\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-2\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(26, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(26, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)