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Properties

Label 50.15
Level 50
Weight 15
Dimension 322
Nonzero newspaces 2
Sturm bound 2250
Trace bound 1

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Defining parameters

Level: \( N \) = \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 2 \)
Sturm bound: \(2250\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(50))\).

Total New Old
Modular forms 1078 322 756
Cusp forms 1022 322 700
Eisenstein series 56 0 56

Trace form

\( 322 q - 256 q^{2} - 8632 q^{3} + 18360 q^{5} + 386048 q^{6} - 4552808 q^{7} + 2097152 q^{8} + O(q^{10}) \) \( 322 q - 256 q^{2} - 8632 q^{3} + 18360 q^{5} + 386048 q^{6} - 4552808 q^{7} + 2097152 q^{8} + 7162240 q^{10} + 74770624 q^{11} - 70713344 q^{12} + 125356908 q^{13} - 274242020 q^{15} + 1879048192 q^{16} + 168949392 q^{17} + 1606368896 q^{18} - 7674763400 q^{19} + 915374080 q^{20} + 11761747784 q^{21} - 9781937152 q^{22} + 34372448 q^{23} + 52476076010 q^{25} + 1203826688 q^{26} - 86806598140 q^{27} - 4334813184 q^{28} + 66244179400 q^{29} + 102898836480 q^{30} - 102388912056 q^{31} - 25769803776 q^{32} + 373263543176 q^{33} + 419654128000 q^{34} - 748413848360 q^{35} - 617053978624 q^{36} + 572595941232 q^{37} + 689941089280 q^{38} - 612540770800 q^{39} - 133593825280 q^{40} - 262937805856 q^{41} + 261758814208 q^{42} + 3082800885528 q^{43} + 696460365330 q^{45} - 1190974815232 q^{46} + 2875939011032 q^{47} + 579283714048 q^{48} + 298566300800 q^{50} - 729996072776 q^{51} + 1026923790336 q^{52} - 2517430557472 q^{53} - 5658183440640 q^{55} + 818199658496 q^{56} + 11705721125280 q^{57} + 6228293642240 q^{58} - 11016799366300 q^{59} + 1778621153280 q^{60} + 4839830055464 q^{61} + 13426156740608 q^{62} + 47276882862188 q^{63} - 29862696530690 q^{65} - 15966647609344 q^{66} - 3761329727848 q^{67} + 13893047812096 q^{68} + 119483021548100 q^{69} + 52161093178880 q^{70} + 6292239093824 q^{71} - 28634846855168 q^{72} - 150521211564012 q^{73} + 234393789109260 q^{75} + 30799205171200 q^{76} + 42261002825984 q^{77} - 104721521604608 q^{78} - 135330281481200 q^{79} - 1232118743040 q^{80} + 223789816695372 q^{81} + 23693028190208 q^{82} + 162106044817508 q^{83} + 224717284147200 q^{84} + 140893448596900 q^{85} - 120250552860672 q^{86} - 506500224342060 q^{87} + 56358678298624 q^{88} + 200556741749150 q^{89} + 456983269851520 q^{90} - 135674539360776 q^{91} - 94670062649344 q^{92} + 1178357926723756 q^{93} - 64310324399560 q^{95} - 25907242729472 q^{96} + 116558666123852 q^{97} - 130291061770496 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(50))\)

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
50.15.c \(\chi_{50}(7, \cdot)\) 50.15.c.a 6 2
50.15.c.b 6
50.15.c.c 6
50.15.c.d 8
50.15.c.e 8
50.15.c.f 8
50.15.f \(\chi_{50}(3, \cdot)\) n/a 280 8

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

Decomposition of \(S_{15}^{\mathrm{old}}(\Gamma_1(50))\) into lower level spaces

\( S_{15}^{\mathrm{old}}(\Gamma_1(50)) \cong \) \(S_{15}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 1}\)