Properties

Label 1053.2
Level 1053
Weight 2
Dimension 31256
Nonzero newspaces 33
Sturm bound 163296
Trace bound 24

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Defining parameters

Level: \( N \) = \( 1053 = 3^{4} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 33 \)
Sturm bound: \(163296\)
Trace bound: \(24\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1053))\).

Total New Old
Modular forms 42120 32488 9632
Cusp forms 39529 31256 8273
Eisenstein series 2591 1232 1359

Trace form

\( 31256 q - 120 q^{2} - 180 q^{3} - 196 q^{4} - 114 q^{5} - 180 q^{6} - 194 q^{7} - 96 q^{8} - 180 q^{9} + O(q^{10}) \) \( 31256 q - 120 q^{2} - 180 q^{3} - 196 q^{4} - 114 q^{5} - 180 q^{6} - 194 q^{7} - 96 q^{8} - 180 q^{9} - 270 q^{10} - 102 q^{11} - 180 q^{12} - 211 q^{13} - 222 q^{14} - 180 q^{15} - 196 q^{16} - 90 q^{17} - 198 q^{18} - 302 q^{19} - 186 q^{20} - 234 q^{21} - 210 q^{22} - 186 q^{23} - 288 q^{24} - 220 q^{25} - 219 q^{26} - 450 q^{27} - 338 q^{28} - 174 q^{29} - 288 q^{30} - 218 q^{31} - 216 q^{32} - 234 q^{33} - 222 q^{34} - 138 q^{35} - 252 q^{36} - 266 q^{37} - 42 q^{38} - 198 q^{39} - 486 q^{40} - 114 q^{41} - 270 q^{42} - 194 q^{43} - 246 q^{44} - 288 q^{45} - 378 q^{46} - 246 q^{47} - 378 q^{48} - 240 q^{49} - 408 q^{50} - 306 q^{51} - 259 q^{52} - 414 q^{53} - 432 q^{54} - 378 q^{55} - 462 q^{56} - 288 q^{57} - 246 q^{58} - 258 q^{59} - 414 q^{60} - 230 q^{61} - 330 q^{62} - 288 q^{63} - 316 q^{64} - 141 q^{65} - 396 q^{66} - 218 q^{67} + 72 q^{68} - 72 q^{69} - 282 q^{70} + 90 q^{71} + 252 q^{72} - 212 q^{73} + 246 q^{74} - 290 q^{76} + 210 q^{77} - 81 q^{78} - 434 q^{79} + 516 q^{80} - 36 q^{81} - 432 q^{82} + 114 q^{83} + 270 q^{84} - 258 q^{85} + 282 q^{86} + 108 q^{87} - 306 q^{88} + 36 q^{89} - 18 q^{90} - 314 q^{91} - 78 q^{92} - 216 q^{93} - 282 q^{94} - 246 q^{95} - 162 q^{96} - 338 q^{97} - 540 q^{98} - 324 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1053))\)

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
1053.2.a \(\chi_{1053}(1, \cdot)\) 1053.2.a.a 1 1
1053.2.a.b 1
1053.2.a.c 1
1053.2.a.d 1
1053.2.a.e 2
1053.2.a.f 2
1053.2.a.g 3
1053.2.a.h 3
1053.2.a.i 4
1053.2.a.j 5
1053.2.a.k 5
1053.2.a.l 6
1053.2.a.m 6
1053.2.a.n 8
1053.2.b \(\chi_{1053}(649, \cdot)\) 1053.2.b.a 2 1
1053.2.b.b 2
1053.2.b.c 2
1053.2.b.d 2
1053.2.b.e 2
1053.2.b.f 2
1053.2.b.g 4
1053.2.b.h 4
1053.2.b.i 10
1053.2.b.j 10
1053.2.b.k 12
1053.2.e \(\chi_{1053}(352, \cdot)\) 1053.2.e.a 2 2
1053.2.e.b 2
1053.2.e.c 2
1053.2.e.d 2
1053.2.e.e 4
1053.2.e.f 4
1053.2.e.g 4
1053.2.e.h 4
1053.2.e.i 4
1053.2.e.j 4
1053.2.e.k 4
1053.2.e.l 4
1053.2.e.m 4
1053.2.e.n 6
1053.2.e.o 6
1053.2.e.p 8
1053.2.e.q 8
1053.2.e.r 8
1053.2.e.s 16
1053.2.f \(\chi_{1053}(217, \cdot)\) n/a 108 2
1053.2.g \(\chi_{1053}(406, \cdot)\) n/a 104 2
1053.2.h \(\chi_{1053}(55, \cdot)\) n/a 108 2
1053.2.i \(\chi_{1053}(161, \cdot)\) n/a 104 2
1053.2.l \(\chi_{1053}(433, \cdot)\) n/a 108 2
1053.2.q \(\chi_{1053}(82, \cdot)\) n/a 104 2
1053.2.r \(\chi_{1053}(595, \cdot)\) n/a 108 2
1053.2.t \(\chi_{1053}(298, \cdot)\) n/a 108 2
1053.2.w \(\chi_{1053}(118, \cdot)\) n/a 216 6
1053.2.x \(\chi_{1053}(289, \cdot)\) n/a 240 6
1053.2.y \(\chi_{1053}(100, \cdot)\) n/a 240 6
1053.2.ba \(\chi_{1053}(215, \cdot)\) n/a 216 4
1053.2.bc \(\chi_{1053}(512, \cdot)\) n/a 216 4
1053.2.bd \(\chi_{1053}(80, \cdot)\) n/a 208 4
1053.2.bf \(\chi_{1053}(188, \cdot)\) n/a 216 4
1053.2.bl \(\chi_{1053}(64, \cdot)\) n/a 240 6
1053.2.bn \(\chi_{1053}(127, \cdot)\) n/a 240 6
1053.2.bo \(\chi_{1053}(10, \cdot)\) n/a 240 6
1053.2.bq \(\chi_{1053}(40, \cdot)\) n/a 1944 18
1053.2.br \(\chi_{1053}(16, \cdot)\) n/a 2232 18
1053.2.bs \(\chi_{1053}(61, \cdot)\) n/a 2232 18
1053.2.bt \(\chi_{1053}(206, \cdot)\) n/a 480 12
1053.2.bw \(\chi_{1053}(8, \cdot)\) n/a 480 12
1053.2.by \(\chi_{1053}(71, \cdot)\) n/a 480 12
1053.2.bz \(\chi_{1053}(43, \cdot)\) n/a 2232 18
1053.2.cd \(\chi_{1053}(25, \cdot)\) n/a 2232 18
1053.2.ce \(\chi_{1053}(4, \cdot)\) n/a 2232 18
1053.2.cl \(\chi_{1053}(5, \cdot)\) n/a 4464 36
1053.2.cm \(\chi_{1053}(20, \cdot)\) n/a 4464 36
1053.2.cn \(\chi_{1053}(2, \cdot)\) n/a 4464 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1053))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1053)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 2}\)