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Properties

Label 1111.2
Level 1111
Weight 2
Dimension 49247
Nonzero newspaces 36
Sturm bound 204000
Trace bound 15

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Defining parameters

Level: \( N \) = \( 1111 = 11 \cdot 101 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(204000\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1111))\).

Total New Old
Modular forms 52000 51031 969
Cusp forms 50001 49247 754
Eisenstein series 1999 1784 215

Trace form

\( 49247 q - 399 q^{2} - 402 q^{3} - 411 q^{4} - 408 q^{5} - 416 q^{6} - 404 q^{7} - 415 q^{8} - 409 q^{9} + O(q^{10}) \) \( 49247 q - 399 q^{2} - 402 q^{3} - 411 q^{4} - 408 q^{5} - 416 q^{6} - 404 q^{7} - 415 q^{8} - 409 q^{9} - 414 q^{10} - 453 q^{11} - 924 q^{12} - 422 q^{13} - 432 q^{14} - 422 q^{15} - 423 q^{16} - 414 q^{17} - 447 q^{18} - 420 q^{19} - 446 q^{20} - 436 q^{21} - 449 q^{22} - 922 q^{23} - 460 q^{24} - 423 q^{25} - 426 q^{26} - 450 q^{27} - 448 q^{28} - 430 q^{29} - 476 q^{30} - 446 q^{31} - 479 q^{32} - 452 q^{33} - 962 q^{34} - 444 q^{35} - 483 q^{36} - 444 q^{37} - 460 q^{38} - 448 q^{39} - 490 q^{40} - 426 q^{41} - 488 q^{42} - 432 q^{43} - 461 q^{44} - 974 q^{45} - 476 q^{46} - 464 q^{47} - 532 q^{48} - 451 q^{49} - 509 q^{50} - 476 q^{51} - 514 q^{52} - 442 q^{53} - 500 q^{54} - 458 q^{55} - 1020 q^{56} - 480 q^{57} - 490 q^{58} - 470 q^{59} - 564 q^{60} - 486 q^{61} - 468 q^{62} - 512 q^{63} - 511 q^{64} - 492 q^{65} - 466 q^{66} - 954 q^{67} - 518 q^{68} - 498 q^{69} - 552 q^{70} - 466 q^{71} - 595 q^{72} - 482 q^{73} - 502 q^{74} - 532 q^{75} - 540 q^{76} - 454 q^{77} - 1084 q^{78} - 460 q^{79} - 578 q^{80} - 523 q^{81} - 508 q^{82} - 372 q^{83} - 32 q^{84} - 304 q^{85} - 356 q^{86} - 20 q^{87} - 165 q^{88} - 820 q^{89} + 158 q^{90} - 196 q^{91} + 436 q^{92} - 114 q^{93} - 112 q^{94} - 120 q^{95} + 564 q^{96} - 184 q^{97} - 183 q^{98} - 59 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1111))\)

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
1111.2.a \(\chi_{1111}(1, \cdot)\) 1111.2.a.a 1 1
1111.2.a.b 1
1111.2.a.c 2
1111.2.a.d 2
1111.2.a.e 9
1111.2.a.f 16
1111.2.a.g 25
1111.2.a.h 27
1111.2.b \(\chi_{1111}(100, \cdot)\) 1111.2.b.a 84 1
1111.2.f \(\chi_{1111}(10, \cdot)\) n/a 200 2
1111.2.g \(\chi_{1111}(137, \cdot)\) n/a 400 4
1111.2.h \(\chi_{1111}(102, \cdot)\) n/a 400 4
1111.2.i \(\chi_{1111}(196, \cdot)\) n/a 400 4
1111.2.j \(\chi_{1111}(188, \cdot)\) n/a 344 4
1111.2.k \(\chi_{1111}(36, \cdot)\) n/a 400 4
1111.2.l \(\chi_{1111}(339, \cdot)\) n/a 400 4
1111.2.n \(\chi_{1111}(115, \cdot)\) n/a 400 4
1111.2.t \(\chi_{1111}(267, \cdot)\) n/a 400 4
1111.2.y \(\chi_{1111}(14, \cdot)\) n/a 400 4
1111.2.z \(\chi_{1111}(201, \cdot)\) n/a 400 4
1111.2.ba \(\chi_{1111}(317, \cdot)\) n/a 400 4
1111.2.bb \(\chi_{1111}(166, \cdot)\) n/a 336 4
1111.2.be \(\chi_{1111}(39, \cdot)\) n/a 800 8
1111.2.bh \(\chi_{1111}(62, \cdot)\) n/a 800 8
1111.2.bi \(\chi_{1111}(140, \cdot)\) n/a 800 8
1111.2.bj \(\chi_{1111}(161, \cdot)\) n/a 800 8
1111.2.bk \(\chi_{1111}(293, \cdot)\) n/a 800 8
1111.2.bp \(\chi_{1111}(32, \cdot)\) n/a 800 8
1111.2.bq \(\chi_{1111}(56, \cdot)\) n/a 1720 20
1111.2.br \(\chi_{1111}(31, \cdot)\) n/a 2000 20
1111.2.bs \(\chi_{1111}(5, \cdot)\) n/a 2000 20
1111.2.bt \(\chi_{1111}(97, \cdot)\) n/a 2000 20
1111.2.bu \(\chi_{1111}(37, \cdot)\) n/a 2000 20
1111.2.bx \(\chi_{1111}(4, \cdot)\) n/a 2000 20
1111.2.by \(\chi_{1111}(82, \cdot)\) n/a 2000 20
1111.2.bz \(\chi_{1111}(23, \cdot)\) n/a 1680 20
1111.2.ca \(\chi_{1111}(49, \cdot)\) n/a 2000 20
1111.2.cj \(\chi_{1111}(9, \cdot)\) n/a 2000 20
1111.2.cl \(\chi_{1111}(7, \cdot)\) n/a 4000 40
1111.2.cm \(\chi_{1111}(2, \cdot)\) n/a 4000 40
1111.2.cn \(\chi_{1111}(28, \cdot)\) n/a 4000 40
1111.2.co \(\chi_{1111}(98, \cdot)\) n/a 4000 40
1111.2.ct \(\chi_{1111}(29, \cdot)\) n/a 4000 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1111))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1111)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(101))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1111))\)\(^{\oplus 1}\)