Properties

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

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Defining parameters

Level: \( N \) = \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newforms: \( 63 \)
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

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

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

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