Properties

Label 15.7
Level 15
Weight 7
Dimension 30
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 112
Trace bound 1

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(112\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(15))\).

Total New Old
Modular forms 56 34 22
Cusp forms 40 30 10
Eisenstein series 16 4 12

Trace form

\( 30q + 16q^{2} + 20q^{3} - 136q^{4} + 136q^{5} + 544q^{6} - 536q^{7} - 3468q^{8} - 2102q^{9} + O(q^{10}) \) \( 30q + 16q^{2} + 20q^{3} - 136q^{4} + 136q^{5} + 544q^{6} - 536q^{7} - 3468q^{8} - 2102q^{9} + 6044q^{10} + 3248q^{11} + 8164q^{12} - 1292q^{13} - 7306q^{15} - 23552q^{16} - 5540q^{17} - 11032q^{18} + 28836q^{19} + 12564q^{20} + 5424q^{21} + 9000q^{22} + 11776q^{23} - 22968q^{24} - 58074q^{25} + 24464q^{26} + 71180q^{27} + 118504q^{28} - 52604q^{30} - 81132q^{31} - 126476q^{32} - 72536q^{33} - 132008q^{34} - 59360q^{35} + 25664q^{36} - 77876q^{37} - 55776q^{38} + 322040q^{39} + 685168q^{40} + 395312q^{41} + 144672q^{42} + 93352q^{43} - 286724q^{45} - 790328q^{46} - 246752q^{47} - 879812q^{48} - 972062q^{49} - 669776q^{50} - 147284q^{51} + 795640q^{52} + 954196q^{53} + 1717456q^{54} + 569136q^{55} + 961920q^{56} + 117368q^{57} + 903048q^{58} - 953144q^{60} + 96276q^{61} - 1459672q^{62} - 1260768q^{63} - 3180024q^{64} - 843212q^{65} - 432208q^{66} + 149320q^{67} + 761696q^{68} + 2447916q^{69} + 3729720q^{70} + 831584q^{71} + 2778444q^{72} + 551836q^{73} - 1866676q^{75} - 2323808q^{76} - 3205552q^{77} - 5396480q^{78} - 2117724q^{79} - 1124876q^{80} + 107350q^{81} - 1579752q^{82} + 1244224q^{83} + 5438520q^{84} + 7760552q^{85} + 8173568q^{86} + 5588096q^{87} + 5712552q^{88} - 6343516q^{90} - 7518256q^{91} - 7092056q^{92} - 5463312q^{93} - 10279928q^{94} - 4466016q^{95} - 2254432q^{96} - 1652180q^{97} + 6386552q^{98} + 5425040q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(15))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
15.7.c \(\chi_{15}(11, \cdot)\) 15.7.c.a 8 1
15.7.d \(\chi_{15}(14, \cdot)\) 15.7.d.a 1 1
15.7.d.b 1
15.7.d.c 8
15.7.f \(\chi_{15}(7, \cdot)\) 15.7.f.a 12 2

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)