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Properties

Label 25.9
Level 25
Weight 9
Dimension 174
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 450
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(450\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(25))\).

Total New Old
Modular forms 214 194 20
Cusp forms 186 174 12
Eisenstein series 28 20 8

Trace form

\( 174 q - 6 q^{2} + 134 q^{3} - 10 q^{4} - 230 q^{5} - 3522 q^{6} + 4694 q^{7} + 16430 q^{8} - 10 q^{9} + O(q^{10}) \) \( 174 q - 6 q^{2} + 134 q^{3} - 10 q^{4} - 230 q^{5} - 3522 q^{6} + 4694 q^{7} + 16430 q^{8} - 10 q^{9} - 30880 q^{10} - 46402 q^{11} + 91814 q^{12} + 238274 q^{13} - 10 q^{14} - 241450 q^{15} - 175106 q^{16} + 160344 q^{17} + 908114 q^{18} + 718890 q^{19} + 340370 q^{20} - 873222 q^{21} - 1951082 q^{22} - 928086 q^{23} + 2032310 q^{25} + 3430588 q^{26} + 1512260 q^{27} - 2303194 q^{28} - 1956910 q^{29} - 4500490 q^{30} - 1695182 q^{31} - 6067866 q^{32} - 3265102 q^{33} + 10303990 q^{34} + 4124560 q^{35} + 1751414 q^{36} + 9988394 q^{37} - 15703000 q^{38} - 22510410 q^{39} - 4123060 q^{40} + 3770558 q^{41} + 47975778 q^{42} + 12790694 q^{43} - 2138860 q^{44} - 33978380 q^{45} - 33395742 q^{46} + 4116294 q^{47} - 11191976 q^{48} + 13239250 q^{50} - 19367932 q^{51} + 94244944 q^{52} + 67226634 q^{53} + 57025140 q^{54} - 14642290 q^{55} - 23503510 q^{56} - 58684970 q^{57} - 73534120 q^{58} + 24222740 q^{59} - 66375070 q^{60} - 75431422 q^{61} - 47131292 q^{62} + 51174964 q^{63} + 112817140 q^{64} + 89469970 q^{65} + 230091246 q^{66} + 107376894 q^{67} - 70381394 q^{68} - 128418860 q^{69} - 177099410 q^{70} - 93421882 q^{71} - 527021640 q^{72} - 283847886 q^{73} + 257329110 q^{75} + 358601220 q^{76} + 266491318 q^{77} + 353875228 q^{78} + 138506190 q^{79} + 245270230 q^{80} + 29349494 q^{81} - 111673122 q^{82} - 648429096 q^{83} - 1517250010 q^{84} - 616093620 q^{85} + 23310938 q^{86} + 627352500 q^{87} + 1331895070 q^{88} + 1051406240 q^{89} + 1480613390 q^{90} + 50148618 q^{91} - 531766206 q^{92} - 811342712 q^{93} - 1160168810 q^{94} - 920404690 q^{95} - 1208622342 q^{96} - 546090006 q^{97} + 178217846 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.9.c \(\chi_{25}(7, \cdot)\) 25.9.c.a 4 2
25.9.c.b 6
25.9.c.c 12
25.9.f \(\chi_{25}(2, \cdot)\) 25.9.f.a 152 8

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)