Properties

Label 450.3
Level 450
Weight 3
Dimension 2628
Nonzero newspaces 12
Sturm bound 32400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(32400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(450))\).

Total New Old
Modular forms 11248 2628 8620
Cusp forms 10352 2628 7724
Eisenstein series 896 0 896

Trace form

\( 2628q + 4q^{2} - 12q^{6} - 14q^{7} - 8q^{8} - 68q^{9} + O(q^{10}) \) \( 2628q + 4q^{2} - 12q^{6} - 14q^{7} - 8q^{8} - 68q^{9} - 54q^{10} - 142q^{11} - 20q^{12} - 70q^{13} + 36q^{14} + 24q^{15} + 16q^{16} + 120q^{17} + 104q^{18} + 48q^{19} + 56q^{20} + 54q^{21} + 84q^{22} - 110q^{23} - 18q^{25} + 64q^{26} - 96q^{27} + 120q^{28} + 218q^{29} + 326q^{31} + 24q^{32} + 598q^{33} + 150q^{34} + 704q^{35} + 268q^{36} - 148q^{37} + 296q^{38} + 1018q^{39} - 12q^{40} + 322q^{41} + 208q^{42} - 262q^{43} - 80q^{45} + 200q^{46} - 578q^{47} - 104q^{48} - 78q^{49} - 242q^{50} - 1224q^{51} + 92q^{52} - 944q^{53} - 924q^{54} + 640q^{55} - 152q^{56} - 1168q^{57} + 76q^{58} + 706q^{59} + 448q^{60} + 490q^{61} + 1216q^{62} + 1734q^{63} - 48q^{64} + 2282q^{65} + 120q^{66} + 958q^{67} + 632q^{68} + 1018q^{69} + 744q^{70} + 640q^{71} - 96q^{72} + 252q^{73} + 72q^{74} + 544q^{75} - 120q^{76} + 70q^{77} - 336q^{78} - 1498q^{79} + 772q^{81} - 916q^{82} - 2054q^{83} - 864q^{84} - 2580q^{85} - 876q^{86} - 2110q^{87} - 328q^{88} - 4550q^{89} - 1984q^{90} - 1420q^{91} - 1220q^{92} - 2234q^{93} - 956q^{94} - 1352q^{95} - 80q^{96} + 130q^{97} - 988q^{98} - 2114q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(450))\)

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
450.3.b \(\chi_{450}(449, \cdot)\) 450.3.b.a 4 1
450.3.b.b 4
450.3.b.c 4
450.3.d \(\chi_{450}(251, \cdot)\) 450.3.d.a 2 1
450.3.d.b 2
450.3.d.c 2
450.3.d.d 2
450.3.d.e 2
450.3.d.f 2
450.3.d.g 2
450.3.g \(\chi_{450}(307, \cdot)\) 450.3.g.a 2 2
450.3.g.b 2
450.3.g.c 2
450.3.g.d 2
450.3.g.e 2
450.3.g.f 4
450.3.g.g 4
450.3.g.h 4
450.3.g.i 4
450.3.g.j 4
450.3.i \(\chi_{450}(101, \cdot)\) 450.3.i.a 4 2
450.3.i.b 4
450.3.i.c 4
450.3.i.d 16
450.3.i.e 16
450.3.i.f 16
450.3.i.g 16
450.3.k \(\chi_{450}(149, \cdot)\) 450.3.k.a 8 2
450.3.k.b 32
450.3.k.c 32
450.3.m \(\chi_{450}(89, \cdot)\) 450.3.m.a 80 4
450.3.n \(\chi_{450}(71, \cdot)\) 450.3.n.a 32 4
450.3.n.b 48
450.3.o \(\chi_{450}(7, \cdot)\) n/a 144 4
450.3.r \(\chi_{450}(37, \cdot)\) n/a 200 8
450.3.t \(\chi_{450}(11, \cdot)\) n/a 480 8
450.3.u \(\chi_{450}(29, \cdot)\) n/a 480 8
450.3.x \(\chi_{450}(13, \cdot)\) n/a 960 16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(450))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(450)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)