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Properties

Label 7.4.c
Level $7$
Weight $4$
Character orbit 7.c
Rep. character $\chi_{7}(2,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $2$
Newform subspaces $1$
Sturm bound $2$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 7.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(7, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\( 2 q - 2 q^{2} - 7 q^{3} + 4 q^{4} - 7 q^{5} + 28 q^{6} + 28 q^{7} - 48 q^{8} - 22 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{2} - 7 q^{3} + 4 q^{4} - 7 q^{5} + 28 q^{6} + 28 q^{7} - 48 q^{8} - 22 q^{9} - 14 q^{10} + 5 q^{11} + 28 q^{12} - 28 q^{13} + 14 q^{14} + 98 q^{15} + 16 q^{16} + 21 q^{17} - 44 q^{18} - 49 q^{19} - 56 q^{20} - 245 q^{21} - 20 q^{22} + 159 q^{23} + 168 q^{24} + 76 q^{25} + 28 q^{26} - 70 q^{27} + 140 q^{28} + 116 q^{29} - 98 q^{30} - 147 q^{31} - 160 q^{32} + 35 q^{33} - 84 q^{34} + 49 q^{35} - 176 q^{36} - 219 q^{37} - 98 q^{38} + 98 q^{39} + 168 q^{40} + 700 q^{41} + 392 q^{42} - 248 q^{43} - 20 q^{44} - 154 q^{45} + 318 q^{46} - 525 q^{47} - 224 q^{48} + 98 q^{49} - 304 q^{50} + 147 q^{51} - 56 q^{52} - 303 q^{53} + 70 q^{54} - 70 q^{55} - 672 q^{56} + 686 q^{57} - 116 q^{58} + 105 q^{59} + 196 q^{60} + 413 q^{61} + 588 q^{62} + 154 q^{63} + 896 q^{64} + 98 q^{65} + 70 q^{66} - 415 q^{67} - 84 q^{68} - 2226 q^{69} - 490 q^{70} - 864 q^{71} + 528 q^{72} + 1113 q^{73} - 438 q^{74} + 532 q^{75} - 392 q^{76} + 175 q^{77} - 392 q^{78} + 103 q^{79} + 112 q^{80} + 839 q^{81} - 700 q^{82} + 2184 q^{83} - 196 q^{84} - 294 q^{85} + 248 q^{86} - 406 q^{87} - 120 q^{88} + 329 q^{89} + 616 q^{90} - 392 q^{91} + 1272 q^{92} - 1029 q^{93} - 1050 q^{94} - 343 q^{95} - 1120 q^{96} - 1764 q^{97} + 1078 q^{98} - 220 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.4.c.a 7.c 7.c $2$ $0.413$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-7\) \(-7\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots\)