Properties

Label 450.2
Level 450
Weight 2
Dimension 1313
Nonzero newspaces 12
Newform subspaces 63
Sturm bound 21600
Trace bound 3

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 63 \)
Sturm bound: \(21600\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(450))\).

Total New Old
Modular forms 5848 1313 4535
Cusp forms 4953 1313 3640
Eisenstein series 895 0 895

Trace form

\( 1313q - 3q^{2} - 3q^{3} - 3q^{4} - 5q^{5} + 3q^{6} - 18q^{7} + 19q^{9} + O(q^{10}) \) \( 1313q - 3q^{2} - 3q^{3} - 3q^{4} - 5q^{5} + 3q^{6} - 18q^{7} + 19q^{9} + 11q^{10} + 43q^{11} + 16q^{12} + 34q^{13} + 46q^{14} + 24q^{15} - 3q^{16} + 74q^{17} + 26q^{18} + 62q^{19} + 16q^{20} + 54q^{21} + 51q^{22} + 94q^{23} - 3q^{24} + 67q^{25} - 4q^{26} + 48q^{27} + 8q^{28} + 70q^{29} + 44q^{31} + 2q^{32} + 7q^{33} + 8q^{34} + 4q^{35} - 29q^{36} + 81q^{37} - 87q^{38} - 128q^{39} + 3q^{40} - 105q^{41} - 128q^{42} + 17q^{43} - 46q^{44} - 80q^{45} + 36q^{46} - 98q^{47} - 29q^{48} + 30q^{49} - 57q^{50} - 87q^{51} - 14q^{52} - 87q^{53} - 87q^{54} + 60q^{55} - 34q^{56} - 61q^{57} - 50q^{58} - 31q^{59} - 32q^{60} - 104q^{61} - 156q^{62} - 84q^{63} - 253q^{65} - 24q^{66} - 189q^{67} - 117q^{68} - 152q^{69} - 216q^{70} - 24q^{71} + 3q^{72} - 190q^{73} - 212q^{74} - 296q^{75} - 31q^{76} - 474q^{77} - 126q^{78} - 188q^{79} - 5q^{80} - 137q^{81} - 178q^{82} - 436q^{83} - 78q^{84} - 185q^{85} - 43q^{86} - 214q^{87} + 11q^{88} - 239q^{89} - 64q^{90} + 24q^{91} - 6q^{92} - 104q^{93} + 38q^{94} + 28q^{95} + 16q^{96} + 123q^{97} + 72q^{98} - 14q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)

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
450.2.a \(\chi_{450}(1, \cdot)\) 450.2.a.a 1 1
450.2.a.b 1
450.2.a.c 1
450.2.a.d 1
450.2.a.e 1
450.2.a.f 1
450.2.a.g 1
450.2.c \(\chi_{450}(199, \cdot)\) 450.2.c.a 2 1
450.2.c.b 2
450.2.c.c 2
450.2.c.d 2
450.2.e \(\chi_{450}(151, \cdot)\) 450.2.e.a 2 2
450.2.e.b 2
450.2.e.c 2
450.2.e.d 2
450.2.e.e 2
450.2.e.f 2
450.2.e.g 2
450.2.e.h 2
450.2.e.i 2
450.2.e.j 4
450.2.e.k 4
450.2.e.l 4
450.2.e.m 4
450.2.e.n 4
450.2.f \(\chi_{450}(107, \cdot)\) 450.2.f.a 4 2
450.2.f.b 4
450.2.f.c 4
450.2.h \(\chi_{450}(91, \cdot)\) 450.2.h.a 4 4
450.2.h.b 4
450.2.h.c 4
450.2.h.d 8
450.2.h.e 8
450.2.h.f 12
450.2.h.g 12
450.2.j \(\chi_{450}(49, \cdot)\) 450.2.j.a 4 2
450.2.j.b 4
450.2.j.c 4
450.2.j.d 4
450.2.j.e 4
450.2.j.f 8
450.2.j.g 8
450.2.l \(\chi_{450}(19, \cdot)\) 450.2.l.a 8 4
450.2.l.b 8
450.2.l.c 16
450.2.l.d 16
450.2.p \(\chi_{450}(257, \cdot)\) 450.2.p.a 8 4
450.2.p.b 8
450.2.p.c 8
450.2.p.d 8
450.2.p.e 8
450.2.p.f 8
450.2.p.g 8
450.2.p.h 16
450.2.q \(\chi_{450}(31, \cdot)\) 450.2.q.a 8 8
450.2.q.b 112
450.2.q.c 120
450.2.s \(\chi_{450}(17, \cdot)\) 450.2.s.a 16 8
450.2.s.b 16
450.2.s.c 16
450.2.s.d 32
450.2.v \(\chi_{450}(79, \cdot)\) 450.2.v.a 240 8
450.2.w \(\chi_{450}(23, \cdot)\) 450.2.w.a 480 16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(450))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(450)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)