Properties

Label 225.2
Level 225
Weight 2
Dimension 1221
Nonzero newspaces 12
Newforms 34
Sturm bound 7200
Trace bound 2

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newforms: \( 34 \)
Sturm bound: \(7200\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(225))\).

Total New Old
Modular forms 2024 1406 618
Cusp forms 1577 1221 356
Eisenstein series 447 185 262

Trace form

\( 1221q - 16q^{2} - 24q^{3} - 8q^{4} - 21q^{5} - 40q^{6} - 6q^{7} - 24q^{8} - 32q^{9} + O(q^{10}) \) \( 1221q - 16q^{2} - 24q^{3} - 8q^{4} - 21q^{5} - 40q^{6} - 6q^{7} - 24q^{8} - 32q^{9} - 75q^{10} - 46q^{11} - 56q^{12} - 26q^{13} - 54q^{14} - 44q^{15} - 56q^{16} - 44q^{17} - 72q^{18} - 70q^{19} - 90q^{20} - 72q^{21} - 86q^{22} - 74q^{23} - 112q^{24} - 63q^{25} - 132q^{26} - 72q^{27} - 166q^{28} - 94q^{29} - 72q^{30} - 58q^{31} - 91q^{32} - 56q^{33} - 83q^{34} - 32q^{35} - 8q^{36} - 99q^{37} - 28q^{38} + 24q^{39} - 57q^{40} + 26q^{41} + 32q^{42} - 6q^{43} + 36q^{44} - 12q^{45} - 142q^{46} + 10q^{47} + 80q^{48} - 91q^{49} - 89q^{50} - 80q^{51} - 144q^{52} - 79q^{53} - 32q^{54} - 142q^{55} - 66q^{56} - 72q^{57} - 152q^{58} - 128q^{59} + 20q^{60} - 66q^{61} - 68q^{62} - 60q^{63} + 22q^{64} + 53q^{65} - 128q^{66} + 42q^{67} + 190q^{68} - 20q^{69} + 150q^{70} - 62q^{71} + 192q^{72} + 34q^{73} + 304q^{74} + 128q^{75} + 52q^{76} + 234q^{77} + 240q^{78} + 114q^{79} + 425q^{80} + 88q^{81} + 170q^{82} + 284q^{83} + 344q^{84} + 21q^{85} + 266q^{86} + 148q^{87} + 90q^{88} + 177q^{89} + 184q^{90} - 86q^{91} + 182q^{92} + 100q^{93} - 182q^{94} - 70q^{95} + 136q^{96} - 174q^{97} + 56q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
225.2.a \(\chi_{225}(1, \cdot)\) 225.2.a.a 1 1
225.2.a.b 1
225.2.a.c 1
225.2.a.d 1
225.2.a.e 1
225.2.a.f 2
225.2.b \(\chi_{225}(199, \cdot)\) 225.2.b.a 2 1
225.2.b.b 2
225.2.b.c 2
225.2.e \(\chi_{225}(76, \cdot)\) 225.2.e.a 2 2
225.2.e.b 6
225.2.e.c 8
225.2.e.d 8
225.2.e.e 8
225.2.f \(\chi_{225}(107, \cdot)\) 225.2.f.a 4 2
225.2.f.b 8
225.2.h \(\chi_{225}(46, \cdot)\) 225.2.h.a 4 4
225.2.h.b 4
225.2.h.c 8
225.2.h.d 12
225.2.h.e 16
225.2.k \(\chi_{225}(49, \cdot)\) 225.2.k.a 4 2
225.2.k.b 12
225.2.k.c 16
225.2.m \(\chi_{225}(19, \cdot)\) 225.2.m.a 8 4
225.2.m.b 16
225.2.m.c 24
225.2.p \(\chi_{225}(32, \cdot)\) 225.2.p.a 16 4
225.2.p.b 16
225.2.p.c 32
225.2.q \(\chi_{225}(16, \cdot)\) 225.2.q.a 224 8
225.2.s \(\chi_{225}(8, \cdot)\) 225.2.s.a 80 8
225.2.u \(\chi_{225}(4, \cdot)\) 225.2.u.a 224 8
225.2.w \(\chi_{225}(2, \cdot)\) 225.2.w.a 448 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(225))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(225)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)