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

Related objects

Downloads

Learn more about

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

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

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 \(-10\) \(30\) \(-70\) \(550\) \(q+(-2+2\beta _{1}+\beta _{3})q^{2}+(7+8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)