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Properties

Label 900.4
Level 900
Weight 4
Dimension 27396
Nonzero newspaces 24
Sturm bound 172800
Trace bound 16

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Defining parameters

Level: \( N \) = \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(172800\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(900))\).

Total New Old
Modular forms 65920 27764 38156
Cusp forms 63680 27396 36284
Eisenstein series 2240 368 1872

Trace form

\( 27396 q - 21 q^{2} - 3 q^{3} - 11 q^{4} - 67 q^{5} - 19 q^{6} + 34 q^{7} + 66 q^{8} - 131 q^{9} + O(q^{10}) \) \( 27396 q - 21 q^{2} - 3 q^{3} - 11 q^{4} - 67 q^{5} - 19 q^{6} + 34 q^{7} + 66 q^{8} - 131 q^{9} + 119 q^{11} - 30 q^{12} + 156 q^{13} - 84 q^{14} + 168 q^{15} - 143 q^{16} + 12 q^{17} - 80 q^{18} - 134 q^{19} + 170 q^{20} - 86 q^{21} + 521 q^{22} + 386 q^{23} + 35 q^{24} + 303 q^{25} - 1324 q^{26} - 456 q^{27} - 1406 q^{28} - 1600 q^{29} - 1192 q^{30} - 1512 q^{31} - 1751 q^{32} - 455 q^{33} - 1185 q^{34} - 28 q^{35} + 1815 q^{36} + 717 q^{37} + 4847 q^{38} + 796 q^{39} + 2780 q^{40} + 1295 q^{41} + 2220 q^{42} + 1845 q^{43} - 1360 q^{44} - 824 q^{45} - 2862 q^{46} - 382 q^{47} - 5267 q^{48} + 449 q^{49} - 4702 q^{50} - 1359 q^{51} - 2952 q^{52} - 4627 q^{53} - 29 q^{54} - 3572 q^{55} + 2968 q^{56} - 3 q^{57} + 7150 q^{58} + 1381 q^{59} + 3508 q^{60} - 7310 q^{61} + 13296 q^{62} + 3120 q^{63} + 11758 q^{64} + 2139 q^{65} + 4978 q^{66} + 991 q^{67} + 6463 q^{68} - 260 q^{69} - 66 q^{70} + 5664 q^{71} - 10501 q^{72} + 4000 q^{73} - 19530 q^{74} - 13832 q^{75} - 2051 q^{76} - 7314 q^{77} - 8276 q^{78} - 1016 q^{79} - 3182 q^{80} + 3929 q^{81} - 12220 q^{82} + 5704 q^{83} + 11550 q^{84} + 3989 q^{85} + 2843 q^{86} + 11966 q^{87} - 15451 q^{88} + 16447 q^{89} + 13496 q^{90} - 8200 q^{91} + 10826 q^{92} + 15040 q^{93} - 3214 q^{94} + 1052 q^{95} + 9596 q^{96} - 13113 q^{97} + 9890 q^{98} + 2722 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(900))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
900.4.a \(\chi_{900}(1, \cdot)\) 900.4.a.a 1 1
900.4.a.b 1
900.4.a.c 1
900.4.a.d 1
900.4.a.e 1
900.4.a.f 1
900.4.a.g 1
900.4.a.h 1
900.4.a.i 1
900.4.a.j 1
900.4.a.k 1
900.4.a.l 1
900.4.a.m 1
900.4.a.n 1
900.4.a.o 1
900.4.a.p 1
900.4.a.q 1
900.4.a.r 1
900.4.a.s 2
900.4.a.t 4
900.4.d \(\chi_{900}(649, \cdot)\) 900.4.d.a 2 1
900.4.d.b 2
900.4.d.c 2
900.4.d.d 2
900.4.d.e 2
900.4.d.f 2
900.4.d.g 2
900.4.d.h 2
900.4.d.i 2
900.4.d.j 2
900.4.d.k 2
900.4.e \(\chi_{900}(251, \cdot)\) n/a 114 1
900.4.h \(\chi_{900}(899, \cdot)\) n/a 108 1
900.4.i \(\chi_{900}(301, \cdot)\) n/a 114 2
900.4.j \(\chi_{900}(557, \cdot)\) 900.4.j.a 8 2
900.4.j.b 12
900.4.j.c 16
900.4.k \(\chi_{900}(307, \cdot)\) n/a 266 2
900.4.n \(\chi_{900}(181, \cdot)\) n/a 148 4
900.4.o \(\chi_{900}(299, \cdot)\) n/a 640 2
900.4.r \(\chi_{900}(551, \cdot)\) n/a 672 2
900.4.s \(\chi_{900}(49, \cdot)\) n/a 108 2
900.4.v \(\chi_{900}(71, \cdot)\) n/a 720 4
900.4.w \(\chi_{900}(109, \cdot)\) n/a 152 4
900.4.z \(\chi_{900}(179, \cdot)\) n/a 720 4
900.4.be \(\chi_{900}(257, \cdot)\) n/a 216 4
900.4.bf \(\chi_{900}(7, \cdot)\) n/a 1280 4
900.4.bg \(\chi_{900}(61, \cdot)\) n/a 720 8
900.4.bj \(\chi_{900}(127, \cdot)\) n/a 1784 8
900.4.bk \(\chi_{900}(17, \cdot)\) n/a 240 8
900.4.bn \(\chi_{900}(59, \cdot)\) n/a 4288 8
900.4.bq \(\chi_{900}(169, \cdot)\) n/a 720 8
900.4.br \(\chi_{900}(11, \cdot)\) n/a 4288 8
900.4.bs \(\chi_{900}(67, \cdot)\) n/a 8576 16
900.4.bt \(\chi_{900}(77, \cdot)\) n/a 1440 16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(900))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(900)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 27}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(900))\)\(^{\oplus 1}\)