Properties

Label 25.3
Level 25
Weight 3
Dimension 36
Nonzero newspaces 2
Newforms 2
Sturm bound 150
Trace bound 1

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Defining parameters

Level: \( N \) = \( 25 = 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
Sturm bound: \(150\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(25))\).

Total New Old
Modular forms 64 56 8
Cusp forms 36 36 0
Eisenstein series 28 20 8

Trace form

\(36q \) \(\mathstrut -\mathstrut 10q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut -\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 10q^{8} \) \(\mathstrut -\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(36q \) \(\mathstrut -\mathstrut 10q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut -\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 10q^{8} \) \(\mathstrut -\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 10q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 46q^{16} \) \(\mathstrut +\mathstrut 60q^{17} \) \(\mathstrut +\mathstrut 140q^{18} \) \(\mathstrut +\mathstrut 90q^{19} \) \(\mathstrut +\mathstrut 130q^{20} \) \(\mathstrut +\mathstrut 42q^{21} \) \(\mathstrut +\mathstrut 70q^{22} \) \(\mathstrut +\mathstrut 10q^{23} \) \(\mathstrut -\mathstrut 40q^{25} \) \(\mathstrut -\mathstrut 68q^{26} \) \(\mathstrut -\mathstrut 100q^{27} \) \(\mathstrut -\mathstrut 250q^{28} \) \(\mathstrut -\mathstrut 110q^{29} \) \(\mathstrut -\mathstrut 250q^{30} \) \(\mathstrut -\mathstrut 158q^{31} \) \(\mathstrut -\mathstrut 290q^{32} \) \(\mathstrut -\mathstrut 190q^{33} \) \(\mathstrut -\mathstrut 260q^{34} \) \(\mathstrut -\mathstrut 120q^{35} \) \(\mathstrut -\mathstrut 34q^{36} \) \(\mathstrut +\mathstrut 50q^{37} \) \(\mathstrut +\mathstrut 320q^{38} \) \(\mathstrut +\mathstrut 390q^{39} \) \(\mathstrut +\mathstrut 440q^{40} \) \(\mathstrut +\mathstrut 142q^{41} \) \(\mathstrut +\mathstrut 690q^{42} \) \(\mathstrut +\mathstrut 230q^{43} \) \(\mathstrut +\mathstrut 340q^{44} \) \(\mathstrut +\mathstrut 310q^{45} \) \(\mathstrut +\mathstrut 162q^{46} \) \(\mathstrut +\mathstrut 70q^{47} \) \(\mathstrut +\mathstrut 160q^{48} \) \(\mathstrut -\mathstrut 100q^{50} \) \(\mathstrut -\mathstrut 148q^{51} \) \(\mathstrut -\mathstrut 320q^{52} \) \(\mathstrut -\mathstrut 190q^{53} \) \(\mathstrut -\mathstrut 660q^{54} \) \(\mathstrut -\mathstrut 250q^{55} \) \(\mathstrut -\mathstrut 310q^{56} \) \(\mathstrut -\mathstrut 650q^{57} \) \(\mathstrut -\mathstrut 640q^{58} \) \(\mathstrut -\mathstrut 260q^{59} \) \(\mathstrut -\mathstrut 550q^{60} \) \(\mathstrut +\mathstrut 2q^{61} \) \(\mathstrut +\mathstrut 60q^{62} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut +\mathstrut 340q^{64} \) \(\mathstrut +\mathstrut 360q^{65} \) \(\mathstrut +\mathstrut 174q^{66} \) \(\mathstrut +\mathstrut 270q^{67} \) \(\mathstrut +\mathstrut 710q^{68} \) \(\mathstrut +\mathstrut 340q^{69} \) \(\mathstrut +\mathstrut 310q^{70} \) \(\mathstrut +\mathstrut 102q^{71} \) \(\mathstrut +\mathstrut 360q^{72} \) \(\mathstrut +\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 90q^{75} \) \(\mathstrut -\mathstrut 60q^{76} \) \(\mathstrut -\mathstrut 250q^{77} \) \(\mathstrut -\mathstrut 500q^{78} \) \(\mathstrut -\mathstrut 210q^{79} \) \(\mathstrut -\mathstrut 850q^{80} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut +\mathstrut 30q^{82} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut +\mathstrut 600q^{85} \) \(\mathstrut +\mathstrut 42q^{86} \) \(\mathstrut +\mathstrut 300q^{87} \) \(\mathstrut +\mathstrut 190q^{88} \) \(\mathstrut -\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 380q^{90} \) \(\mathstrut +\mathstrut 282q^{91} \) \(\mathstrut -\mathstrut 30q^{92} \) \(\mathstrut +\mathstrut 520q^{93} \) \(\mathstrut +\mathstrut 790q^{94} \) \(\mathstrut +\mathstrut 310q^{95} \) \(\mathstrut +\mathstrut 282q^{96} \) \(\mathstrut +\mathstrut 270q^{97} \) \(\mathstrut +\mathstrut 170q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)

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
25.3.c \(\chi_{25}(7, \cdot)\) 25.3.c.a 4 2
25.3.f \(\chi_{25}(2, \cdot)\) 25.3.f.a 32 8