Properties

Label 1083.2
Level 1083
Weight 2
Dimension 31843
Nonzero newspaces 12
Sturm bound 173280
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1083 = 3 \cdot 19^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(173280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1083))\).

Total New Old
Modular forms 44328 32779 11549
Cusp forms 42313 31843 10470
Eisenstein series 2015 936 1079

Trace form

\( 31843 q + 3 q^{2} - 152 q^{3} - 299 q^{4} + 6 q^{5} - 150 q^{6} - 298 q^{7} + 15 q^{8} - 152 q^{9} + O(q^{10}) \) \( 31843 q + 3 q^{2} - 152 q^{3} - 299 q^{4} + 6 q^{5} - 150 q^{6} - 298 q^{7} + 15 q^{8} - 152 q^{9} - 288 q^{10} + 12 q^{11} - 170 q^{12} - 340 q^{13} - 48 q^{14} - 183 q^{15} - 419 q^{16} - 18 q^{17} - 168 q^{18} - 366 q^{19} - 102 q^{20} - 187 q^{21} - 378 q^{22} - 12 q^{23} - 210 q^{24} - 347 q^{25} - 30 q^{26} - 176 q^{27} - 406 q^{28} - 42 q^{29} - 261 q^{30} - 346 q^{31} - 117 q^{32} - 249 q^{33} - 432 q^{34} - 96 q^{35} - 290 q^{36} - 376 q^{37} - 126 q^{38} - 391 q^{39} - 540 q^{40} - 30 q^{41} - 309 q^{42} - 406 q^{43} - 96 q^{44} - 201 q^{45} - 414 q^{46} - 24 q^{47} - 122 q^{48} - 321 q^{49} - 15 q^{50} - 63 q^{51} - 208 q^{52} + 54 q^{53} - 42 q^{54} - 234 q^{55} + 120 q^{56} - 117 q^{57} - 504 q^{58} + 60 q^{59} + 15 q^{60} - 364 q^{61} - 84 q^{62} - 97 q^{63} - 467 q^{64} - 132 q^{65} - 117 q^{66} - 526 q^{67} - 126 q^{68} - 219 q^{69} - 594 q^{70} - 72 q^{71} - 264 q^{72} - 556 q^{73} - 174 q^{74} - 308 q^{75} - 504 q^{76} - 300 q^{77} - 399 q^{78} - 634 q^{79} - 318 q^{80} - 224 q^{81} - 864 q^{82} - 168 q^{83} - 529 q^{84} - 630 q^{85} - 264 q^{86} - 411 q^{87} - 774 q^{88} - 234 q^{89} - 261 q^{90} - 530 q^{91} - 300 q^{92} - 325 q^{93} - 558 q^{94} - 54 q^{95} - 378 q^{96} - 316 q^{97} - 117 q^{98} - 159 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)

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
1083.2.a \(\chi_{1083}(1, \cdot)\) 1083.2.a.a 1 1
1083.2.a.b 1
1083.2.a.c 1
1083.2.a.d 1
1083.2.a.e 1
1083.2.a.f 2
1083.2.a.g 2
1083.2.a.h 2
1083.2.a.i 2
1083.2.a.j 2
1083.2.a.k 2
1083.2.a.l 3
1083.2.a.m 3
1083.2.a.n 3
1083.2.a.o 3
1083.2.a.p 6
1083.2.a.q 6
1083.2.a.r 8
1083.2.a.s 8
1083.2.d \(\chi_{1083}(1082, \cdot)\) 1083.2.d.a 6 1
1083.2.d.b 8
1083.2.d.c 12
1083.2.d.d 24
1083.2.d.e 48
1083.2.e \(\chi_{1083}(292, \cdot)\) n/a 112 2
1083.2.f \(\chi_{1083}(293, \cdot)\) n/a 196 2
1083.2.i \(\chi_{1083}(28, \cdot)\) n/a 342 6
1083.2.j \(\chi_{1083}(116, \cdot)\) n/a 582 6
1083.2.m \(\chi_{1083}(58, \cdot)\) n/a 1152 18
1083.2.n \(\chi_{1083}(56, \cdot)\) n/a 2232 18
1083.2.q \(\chi_{1083}(7, \cdot)\) n/a 2304 36
1083.2.t \(\chi_{1083}(8, \cdot)\) n/a 4464 36
1083.2.u \(\chi_{1083}(4, \cdot)\) n/a 6804 108
1083.2.x \(\chi_{1083}(2, \cdot)\) n/a 13500 108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1083))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1083)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 1}\)