Properties

Label 1350.3
Level 1350
Weight 3
Dimension 23594
Nonzero newspaces 18
Sturm bound 291600
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(291600\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1350))\).

Total New Old
Modular forms 98880 23594 75286
Cusp forms 95520 23594 71926
Eisenstein series 3360 0 3360

Trace form

\( 23594 q + 12 q^{6} + 12 q^{7} - 12 q^{9} + O(q^{10}) \) \( 23594 q + 12 q^{6} + 12 q^{7} - 12 q^{9} + 32 q^{10} + 60 q^{11} - 12 q^{12} + 20 q^{13} - 72 q^{14} - 144 q^{17} - 48 q^{18} - 142 q^{19} - 48 q^{20} - 228 q^{21} - 80 q^{22} - 150 q^{23} + 64 q^{25} + 54 q^{27} - 12 q^{28} + 126 q^{29} - 136 q^{31} - 204 q^{33} - 616 q^{34} - 1224 q^{35} - 216 q^{36} - 850 q^{37} - 1188 q^{38} - 1098 q^{39} - 128 q^{40} - 1116 q^{41} - 336 q^{42} - 184 q^{43} + 120 q^{45} + 144 q^{46} + 960 q^{47} + 168 q^{48} + 1452 q^{49} + 960 q^{50} + 1290 q^{51} + 536 q^{52} + 3696 q^{53} + 1404 q^{54} + 592 q^{55} + 816 q^{56} + 1944 q^{57} + 872 q^{58} + 966 q^{59} - 244 q^{61} - 864 q^{62} + 318 q^{63} + 96 q^{64} - 1536 q^{65} - 432 q^{66} - 1666 q^{67} - 684 q^{68} - 522 q^{69} - 512 q^{70} - 1032 q^{71} - 192 q^{72} - 1620 q^{73} - 576 q^{74} - 1008 q^{75} - 196 q^{76} - 3516 q^{77} - 288 q^{78} - 1184 q^{79} - 1212 q^{81} + 960 q^{82} + 84 q^{83} + 216 q^{84} + 1088 q^{85} + 1224 q^{86} + 582 q^{87} + 376 q^{88} + 3648 q^{89} + 1820 q^{91} + 1176 q^{92} + 1614 q^{93} + 1252 q^{94} + 1776 q^{95} + 96 q^{96} + 2570 q^{97} + 1224 q^{98} + 2526 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1350))\)

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
1350.3.b \(\chi_{1350}(1349, \cdot)\) 1350.3.b.a 4 1
1350.3.b.b 4
1350.3.b.c 4
1350.3.b.d 4
1350.3.b.e 4
1350.3.b.f 4
1350.3.b.g 8
1350.3.b.h 8
1350.3.b.i 8
1350.3.d \(\chi_{1350}(701, \cdot)\) 1350.3.d.a 2 1
1350.3.d.b 2
1350.3.d.c 2
1350.3.d.d 2
1350.3.d.e 2
1350.3.d.f 2
1350.3.d.g 2
1350.3.d.h 2
1350.3.d.i 2
1350.3.d.j 2
1350.3.d.k 2
1350.3.d.l 4
1350.3.d.m 4
1350.3.d.n 4
1350.3.d.o 8
1350.3.d.p 8
1350.3.g \(\chi_{1350}(757, \cdot)\) 1350.3.g.a 4 2
1350.3.g.b 4
1350.3.g.c 4
1350.3.g.d 4
1350.3.g.e 4
1350.3.g.f 4
1350.3.g.g 4
1350.3.g.h 4
1350.3.g.i 4
1350.3.g.j 4
1350.3.g.k 4
1350.3.g.l 4
1350.3.g.m 8
1350.3.g.n 8
1350.3.g.o 8
1350.3.g.p 8
1350.3.g.q 8
1350.3.g.r 8
1350.3.i \(\chi_{1350}(251, \cdot)\) 1350.3.i.a 4 2
1350.3.i.b 4
1350.3.i.c 4
1350.3.i.d 16
1350.3.i.e 16
1350.3.i.f 16
1350.3.i.g 16
1350.3.k \(\chi_{1350}(449, \cdot)\) 1350.3.k.a 8 2
1350.3.k.b 32
1350.3.k.c 32
1350.3.n \(\chi_{1350}(269, \cdot)\) n/a 320 4
1350.3.o \(\chi_{1350}(161, \cdot)\) n/a 320 4
1350.3.p \(\chi_{1350}(307, \cdot)\) n/a 144 4
1350.3.s \(\chi_{1350}(149, \cdot)\) n/a 648 6
1350.3.t \(\chi_{1350}(101, \cdot)\) n/a 684 6
1350.3.v \(\chi_{1350}(163, \cdot)\) n/a 640 8
1350.3.x \(\chi_{1350}(71, \cdot)\) n/a 480 8
1350.3.y \(\chi_{1350}(89, \cdot)\) n/a 480 8
1350.3.ba \(\chi_{1350}(7, \cdot)\) n/a 1296 12
1350.3.be \(\chi_{1350}(37, \cdot)\) n/a 960 16
1350.3.bg \(\chi_{1350}(11, \cdot)\) n/a 4320 24
1350.3.bh \(\chi_{1350}(29, \cdot)\) n/a 4320 24
1350.3.bj \(\chi_{1350}(13, \cdot)\) n/a 8640 48

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1350))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(1350)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(270))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(675))\)\(^{\oplus 2}\)