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Properties

Label 5.24
Level 5
Weight 24
Dimension 17
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 48
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 24 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_1(5))\).

Total New Old
Modular forms 25 19 6
Cusp forms 21 17 4
Eisenstein series 4 2 2

Trace form

\( 17 q - 114 q^{2} - 346108 q^{3} - 38070404 q^{4} + 75933625 q^{5} + 512824144 q^{6} - 3443393944 q^{7} - 103805143320 q^{8} + 48405803209 q^{9} + O(q^{10}) \) \( 17 q - 114 q^{2} - 346108 q^{3} - 38070404 q^{4} + 75933625 q^{5} + 512824144 q^{6} - 3443393944 q^{7} - 103805143320 q^{8} + 48405803209 q^{9} - 922142730250 q^{10} - 1103152603356 q^{11} - 3122068671104 q^{12} - 17708827677958 q^{13} + 87371575065432 q^{14} - 11282824394500 q^{15} + 352420747281072 q^{16} - 400773679253154 q^{17} + 1055883250070582 q^{18} + 1023732444488380 q^{19} - 3446193497286500 q^{20} + 1589556780048264 q^{21} + 4922781627076152 q^{22} - 8977687417674408 q^{23} + 68569836140823840 q^{24} + 1252591568140625 q^{25} - 67812591831492876 q^{26} + 27122419710266120 q^{27} - 41857900826905072 q^{28} - 6209038098357930 q^{29} - 325012705813874000 q^{30} - 272648129641509536 q^{31} - 397223410428571104 q^{32} - 90065269669987856 q^{33} + 635770211722581052 q^{34} + 498625203424856000 q^{35} + 2622069587003869532 q^{36} - 21334199693948974 q^{37} - 1795169170731922680 q^{38} - 5077716711058048312 q^{39} + 13240663480160065000 q^{40} - 9270890925176107926 q^{41} + 6912093180523506672 q^{42} + 7907154864585073292 q^{43} - 11766240120366108528 q^{44} - 19929858828563780375 q^{45} + 49959196928132018104 q^{46} - 13204918525622353584 q^{47} - 18904412815955921408 q^{48} + 132912815428142801821 q^{49} - 96728153804764031250 q^{50} - 256246308404005223096 q^{51} - 118547810756431702504 q^{52} + 90794495767259969442 q^{53} - 137230529120446085120 q^{54} - 24964360485373561500 q^{55} + 351348606289704424320 q^{56} + 318170994314553099440 q^{57} - 37875543910733728620 q^{58} + 257593259923941440340 q^{59} + 1160208847672510276000 q^{60} - 226451584099972190906 q^{61} - 369590564125830216288 q^{62} + 623776188049570308072 q^{63} - 566613801345405980224 q^{64} + 921748092206016859250 q^{65} - 2639185489318281796192 q^{66} - 3717076454064678430204 q^{67} - 1742532756566546375352 q^{68} + 5349397039295455759848 q^{69} - 441044649421378233000 q^{70} - 5318332894843151226696 q^{71} - 3890481728057153637240 q^{72} + 5856780332558024081942 q^{73} + 22402296752648518244292 q^{74} - 2093366176026830687500 q^{75} - 24931556038491368739760 q^{76} - 10234467674662676913408 q^{77} + 1244369973506079002704 q^{78} + 20662624877609670547120 q^{79} + 41483099617811882638000 q^{80} - 57907254098762016551663 q^{81} - 37671201695425413475908 q^{82} + 34715943101214709600692 q^{83} + 101565928305351812939232 q^{84} + 37653110097115577009750 q^{85} - 84232688413995117647136 q^{86} - 128435906109488996520040 q^{87} + 57148008582119360753760 q^{88} + 122332121688434459177610 q^{89} + 137258832438168651896750 q^{90} - 164311534624076592366656 q^{91} - 244361178244195179634704 q^{92} + 97039420325706754786464 q^{93} + 289588714109170952011912 q^{94} + 185325586393580712417500 q^{95} - 1075496665539911093074816 q^{96} - 372748239348536846288434 q^{97} + 121814749446938910095598 q^{98} + 1093390457057052087918788 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_1(5))\)

We only show spaces with even 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
5.24.a \(\chi_{5}(1, \cdot)\) 5.24.a.a 3 1
5.24.a.b 4
5.24.b \(\chi_{5}(4, \cdot)\) 5.24.b.a 10 1

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_1(5))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_1(5)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)