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

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

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 the 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

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