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Properties

Label 25.10
Level 25
Weight 10
Dimension 197
Nonzero newspaces 4
Newform subspaces 10
Sturm bound 500
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 10 \)
Sturm bound: \(500\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(25))\).

Total New Old
Modular forms 239 218 21
Cusp forms 211 197 14
Eisenstein series 28 21 7

Trace form

\( 197 q + 26 q^{2} - 302 q^{3} + 1534 q^{4} - 1775 q^{5} + 3214 q^{6} - 11894 q^{7} + 25190 q^{8} - 14904 q^{9} + O(q^{10}) \) \( 197 q + 26 q^{2} - 302 q^{3} + 1534 q^{4} - 1775 q^{5} + 3214 q^{6} - 11894 q^{7} + 25190 q^{8} - 14904 q^{9} + 70400 q^{10} - 175506 q^{11} - 454314 q^{12} + 1818 q^{13} + 1797638 q^{14} + 162960 q^{15} - 4022898 q^{16} - 305894 q^{17} - 607622 q^{18} + 1635350 q^{19} + 5586410 q^{20} - 4174266 q^{21} - 4763738 q^{22} - 155382 q^{23} - 7528340 q^{24} - 7141265 q^{25} - 6581316 q^{26} + 13939210 q^{27} + 30852022 q^{28} + 11741490 q^{29} - 18521930 q^{30} + 1252894 q^{31} - 28564554 q^{32} + 7870806 q^{33} - 28518802 q^{34} - 1807960 q^{35} + 40796982 q^{36} + 15309381 q^{37} + 114225260 q^{38} + 3597222 q^{39} - 147465460 q^{40} - 5397866 q^{41} - 29250758 q^{42} - 28065862 q^{43} + 236348968 q^{44} + 252763505 q^{45} + 141597994 q^{46} - 95150894 q^{47} - 474300012 q^{48} - 147164151 q^{49} - 296219950 q^{50} - 182418336 q^{51} - 70041084 q^{52} + 295474253 q^{53} + 1088861840 q^{54} + 311889870 q^{55} - 393637550 q^{56} - 482446090 q^{57} - 351622780 q^{58} + 46871130 q^{59} - 120766990 q^{60} + 168620734 q^{61} + 274492272 q^{62} - 14922322 q^{63} - 1443524136 q^{64} - 1598125945 q^{65} - 876432082 q^{66} + 689769226 q^{67} + 3225529382 q^{68} + 2419745542 q^{69} + 1881992270 q^{70} + 530670374 q^{71} - 1562593080 q^{72} - 2049558102 q^{73} - 6631076892 q^{74} - 2916728540 q^{75} + 253548420 q^{76} + 1921698582 q^{77} + 3361105976 q^{78} + 2614262070 q^{79} + 5408991110 q^{80} + 1790266452 q^{81} + 2935692102 q^{82} + 781861398 q^{83} - 3457426522 q^{84} - 4035826615 q^{85} - 2723757126 q^{86} - 8104003990 q^{87} - 8306215810 q^{88} + 1920727575 q^{89} + 11577233550 q^{90} + 5775589774 q^{91} + 9208664226 q^{92} + 4750859686 q^{93} + 4533024518 q^{94} + 248605210 q^{95} - 5295840886 q^{96} - 8831007394 q^{97} - 10373469818 q^{98} - 6760099788 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.10.a \(\chi_{25}(1, \cdot)\) 25.10.a.a 1 1
25.10.a.b 2
25.10.a.c 3
25.10.a.d 3
25.10.a.e 4
25.10.b \(\chi_{25}(24, \cdot)\) 25.10.b.a 2 1
25.10.b.b 4
25.10.b.c 6
25.10.d \(\chi_{25}(6, \cdot)\) 25.10.d.a 84 4
25.10.e \(\chi_{25}(4, \cdot)\) 25.10.e.a 88 4

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)