↑

Properties

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

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

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