↑

Properties

Label 29.15
Level 29
Weight 15
Dimension 476
Nonzero newspaces 2
Sturm bound 1050
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 29 \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 2 \)
Sturm bound: \(1050\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(29))\).

Total New Old
Modular forms 504 504 0
Cusp forms 476 476 0
Eisenstein series 28 28 0

Trace form

\( 476 q - 14 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 14 q^{7} - 14 q^{8} - 14 q^{9} + O(q^{10}) \) \( 476 q - 14 q^{2} - 14 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 14 q^{7} - 14 q^{8} - 14 q^{9} - 14 q^{10} - 14 q^{11} - 14 q^{12} - 14 q^{13} - 14 q^{14} - 14 q^{15} - 14 q^{16} - 14 q^{17} - 14 q^{18} - 14 q^{19} + 2773843954 q^{20} - 6617991562 q^{21} - 5556730382 q^{22} + 11465109096 q^{23} - 33206304782 q^{24} - 32314443770 q^{25} + 20752538226 q^{26} + 82867848364 q^{27} - 86838515050 q^{29} - 184414852636 q^{30} + 90037989118 q^{31} + 341986770930 q^{32} - 7049034944 q^{33} - 352509467534 q^{34} - 201283791730 q^{35} + 1047036297202 q^{36} + 255911074132 q^{37} - 557472688654 q^{38} - 760129258210 q^{39} + 1683282198514 q^{40} - 14 q^{41} - 14 q^{42} - 14 q^{43} + 1097188907528 q^{44} + 899740241806 q^{45} + 4797667044156 q^{46} - 2727052131174 q^{47} - 5681126544926 q^{48} + 5217167545394 q^{49} + 10251429856472 q^{50} - 1644211339358 q^{51} - 16518586855134 q^{52} - 7242085501322 q^{53} + 6111113397844 q^{54} + 22005895437330 q^{55} + 18253884099220 q^{56} - 38829423054422 q^{58} - 8849135296484 q^{59} - 24853638406534 q^{60} + 10843488169682 q^{61} + 45397717267616 q^{62} + 45372799993234 q^{63} - 4330576112576 q^{64} - 36760598981078 q^{65} - 84385717941182 q^{66} - 11681900150494 q^{67} + 76712295782108 q^{68} + 69251528350354 q^{69} - 60863676317822 q^{70} - 16373021103936 q^{71} + 59758782733720 q^{72} + 97790633190222 q^{73} - 269430642507124 q^{74} - 28965380042844 q^{75} + 176040652963826 q^{76} + 141768474554056 q^{77} + 73167915720690 q^{78} - 38069527765738 q^{79} - 486402060877838 q^{80} - 212409716278494 q^{81} + 3762025465842 q^{82} + 124332343902298 q^{83} + 543718186860688 q^{84} + 201438351616390 q^{85} - 193438531737444 q^{87} - 733985935786012 q^{88} - 261654854479424 q^{89} - 120610225517740 q^{90} + 254747020862446 q^{91} + 994419350765554 q^{92} + 331306253437418 q^{93} + 132999323512818 q^{94} - 381563742511742 q^{95} - 2051997204230736 q^{96} - 661254709764964 q^{97} + 761746892263280 q^{98} + 1308410317902100 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(29))\)

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
29.15.c \(\chi_{29}(12, \cdot)\) 29.15.c.a 68 2
29.15.f \(\chi_{29}(2, \cdot)\) n/a 408 12

"n/a" means that newforms for that character have not been added to the database yet