Properties

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 $1$

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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

\( 6 q - 2 q^{2} + 6 q^{3} - 12 q^{4} - 10 q^{5} + 50 q^{7} + 16 q^{8} - 41 q^{9} + O(q^{10}) \) \( 6 q - 2 q^{2} + 6 q^{3} - 12 q^{4} - 10 q^{5} + 50 q^{7} + 16 q^{8} - 41 q^{9} + 18 q^{10} - 18 q^{11} - 48 q^{12} - 61 q^{13} - 160 q^{14} + 104 q^{15} - 48 q^{16} + 103 q^{17} + 308 q^{18} - 78 q^{19} + 20 q^{20} - 52 q^{21} + 16 q^{22} + 154 q^{23} - 476 q^{25} + 150 q^{26} - 396 q^{27} + 200 q^{28} + 211 q^{29} + 184 q^{30} + 352 q^{31} - 32 q^{32} + 806 q^{33} - 628 q^{34} - 256 q^{35} - 164 q^{36} + 279 q^{37} - 288 q^{38} - 1122 q^{39} - 144 q^{40} - 437 q^{41} + 112 q^{42} - 106 q^{43} + 144 q^{44} - 83 q^{45} - 440 q^{46} + 1224 q^{47} + 96 q^{48} - 117 q^{49} - 8 q^{50} + 1964 q^{51} + 464 q^{52} + 166 q^{53} + 936 q^{54} - 768 q^{55} + 320 q^{56} - 676 q^{57} + 370 q^{58} - 102 q^{59} - 832 q^{60} - 829 q^{61} - 768 q^{62} + 912 q^{63} + 384 q^{64} - 255 q^{65} - 2912 q^{66} - 710 q^{67} + 412 q^{68} - 186 q^{69} + 1104 q^{70} + 490 q^{71} - 616 q^{72} - 786 q^{73} + 2250 q^{74} - 1298 q^{75} - 312 q^{76} + 1164 q^{77} + 2424 q^{78} + 3048 q^{79} + 80 q^{80} + 253 q^{81} - 94 q^{82} - 4992 q^{83} + 104 q^{84} + 359 q^{85} - 1168 q^{86} - 1638 q^{87} + 64 q^{88} + 1912 q^{89} + 620 q^{90} - 1994 q^{91} - 1232 q^{92} - 2496 q^{93} + 328 q^{94} - 248 q^{95} + 976 q^{97} - 1506 q^{98} + 4384 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(26, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
26.4.c.a 26.c 13.c $2$ $1.534$ \(\Q(\sqrt{-3}) \) None 26.4.c.a \(2\) \(3\) \(4\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
26.4.c.b 26.c 13.c $4$ $1.534$ \(\Q(\sqrt{-3}, \sqrt{217})\) None 26.4.c.b \(-4\) \(3\) \(-14\) \(45\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-4+4\beta _{2}+\cdots)q^{4}+\cdots\)

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

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