Properties

Label 5.7.c
Level 5
Weight 7
Character orbit c
Rep. character \(\chi_{5}(2,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 4
Newforms 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 7 \)
Character orbit: \([\chi]\) = 5.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(5, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\( 4q - 10q^{2} + 30q^{3} - 70q^{5} - 552q^{6} + 550q^{7} + 1860q^{8} + O(q^{10}) \) \( 4q - 10q^{2} + 30q^{3} - 70q^{5} - 552q^{6} + 550q^{7} + 1860q^{8} - 4370q^{10} - 1052q^{11} + 3480q^{12} + 1960q^{13} - 90q^{15} - 776q^{16} - 3280q^{17} - 870q^{18} + 20340q^{20} + 3828q^{21} - 27520q^{22} - 39010q^{23} + 30400q^{25} + 44068q^{26} + 31320q^{27} - 4840q^{28} - 50640q^{30} - 33172q^{31} - 48760q^{32} + 22260q^{33} - 24970q^{35} - 40836q^{36} + 146860q^{37} + 218040q^{38} - 110100q^{40} - 213932q^{41} - 31680q^{42} - 72050q^{43} + 78210q^{45} + 323288q^{46} + 830q^{47} - 74160q^{48} - 203350q^{50} - 172212q^{51} - 173300q^{52} - 29620q^{53} + 470660q^{55} + 467280q^{56} + 195840q^{57} - 554640q^{58} + 620280q^{60} - 111052q^{61} - 610520q^{62} - 350130q^{63} - 406540q^{65} - 457824q^{66} - 146930q^{67} + 775780q^{68} - 133320q^{70} + 1310188q^{71} + 899460q^{72} + 553540q^{73} - 435450q^{75} - 2073840q^{76} - 476300q^{77} + 268200q^{78} - 1011520q^{80} - 624816q^{81} + 2554880q^{82} + 536870q^{83} - 1344920q^{85} + 1019128q^{86} - 763440q^{87} - 187680q^{88} + 947310q^{90} + 1131548q^{91} - 2552680q^{92} + 444660q^{93} + 912600q^{95} - 568992q^{96} - 59420q^{97} - 1892810q^{98} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(5, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.7.c.a \(4\) \(1.150\) \(\Q(i, \sqrt{201})\) None \(-10\) \(30\) \(-70\) \(550\) \(q+(-2+2\beta _{1}+\beta _{3})q^{2}+(7+8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)