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Properties

Label 15.13
Level 15
Weight 13
Dimension 62
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 208
Trace bound 1

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 13 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(208\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(15))\).

Total New Old
Modular forms 104 66 38
Cusp forms 88 62 26
Eisenstein series 16 4 12

Trace form

\( 62 q + 920 q^{3} + 9112 q^{4} + 8496 q^{5} + 73984 q^{6} - 413200 q^{7} + 956340 q^{8} - 1713002 q^{9} + O(q^{10}) \) \( 62 q + 920 q^{3} + 9112 q^{4} + 8496 q^{5} + 73984 q^{6} - 413200 q^{7} + 956340 q^{8} - 1713002 q^{9} - 2282836 q^{10} + 2280096 q^{11} - 10054700 q^{12} - 7684120 q^{13} + 29781614 q^{15} - 23988480 q^{16} + 9358200 q^{17} + 220351880 q^{18} - 157894484 q^{19} - 428279436 q^{20} - 21576864 q^{21} + 138411720 q^{22} + 725253120 q^{23} - 225113112 q^{24} - 1627214194 q^{25} - 2084949072 q^{26} + 335822120 q^{27} + 6424122440 q^{28} - 3780972044 q^{30} - 3214664180 q^{31} + 8694149940 q^{32} + 2453924560 q^{33} - 617523752 q^{34} - 13149339840 q^{35} + 8713989536 q^{36} - 13740087400 q^{37} + 25374706560 q^{38} + 14252786192 q^{39} - 9286176272 q^{40} - 3043842336 q^{41} - 20480368080 q^{42} - 48405198160 q^{43} + 32683557976 q^{45} + 107798546056 q^{46} - 28337889600 q^{47} - 55186530020 q^{48} - 26364374330 q^{49} - 34577667936 q^{50} - 60948149732 q^{51} + 41261555960 q^{52} - 2949695640 q^{53} + 76427337424 q^{54} + 60540255456 q^{55} + 25647264000 q^{56} - 142630981840 q^{57} - 196007875800 q^{58} + 329058797176 q^{60} + 344223915436 q^{61} + 163013698440 q^{62} + 24724380480 q^{63} - 1054366255480 q^{64} + 31646723688 q^{65} - 101605738096 q^{66} + 76863217520 q^{67} + 636608802240 q^{68} + 720762967644 q^{69} - 164310044520 q^{70} - 483350173632 q^{71} - 1292729930100 q^{72} - 633637002760 q^{73} + 1061885672744 q^{75} + 2373086069600 q^{76} + 1080322578720 q^{77} + 304263861760 q^{78} + 336740197996 q^{79} - 3264958513836 q^{80} - 2883271557458 q^{81} + 966215060280 q^{82} + 1262089900800 q^{83} + 2291544984312 q^{84} - 985901486188 q^{85} - 1188175762944 q^{86} - 886322007040 q^{87} - 339203966040 q^{88} + 797291508644 q^{90} - 4225869736736 q^{91} + 1651508310600 q^{92} - 295334985120 q^{93} - 873638550392 q^{94} + 1628725489344 q^{95} + 3948153458144 q^{96} - 80473865320 q^{97} + 946797702120 q^{98} - 736773615520 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(15))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
15.13.c \(\chi_{15}(11, \cdot)\) 15.13.c.a 16 1
15.13.d \(\chi_{15}(14, \cdot)\) 15.13.d.a 1 1
15.13.d.b 1
15.13.d.c 20
15.13.f \(\chi_{15}(7, \cdot)\) 15.13.f.a 24 2

Decomposition of \(S_{13}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{13}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{13}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 1}\)