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

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

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

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