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Properties

Label 1027.2
Level 1027
Weight 2
Dimension 42297
Nonzero newspaces 30
Sturm bound 174720
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1027 = 13 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(174720\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1027))\).

Total New Old
Modular forms 44616 43993 623
Cusp forms 42745 42297 448
Eisenstein series 1871 1696 175

Trace form

\( 42297 q - 387 q^{2} - 390 q^{3} - 399 q^{4} - 396 q^{5} - 414 q^{6} - 398 q^{7} - 405 q^{8} - 401 q^{9} + O(q^{10}) \) \( 42297 q - 387 q^{2} - 390 q^{3} - 399 q^{4} - 396 q^{5} - 414 q^{6} - 398 q^{7} - 405 q^{8} - 401 q^{9} - 402 q^{10} - 402 q^{11} - 410 q^{12} - 420 q^{13} - 882 q^{14} - 426 q^{15} - 431 q^{16} - 414 q^{17} - 429 q^{18} - 398 q^{19} - 438 q^{20} - 422 q^{21} - 426 q^{22} - 426 q^{23} - 438 q^{24} - 429 q^{25} - 438 q^{26} - 882 q^{27} - 446 q^{28} - 414 q^{29} - 450 q^{30} - 422 q^{31} - 435 q^{32} - 438 q^{33} - 444 q^{34} - 438 q^{35} - 483 q^{36} - 458 q^{37} - 474 q^{38} - 461 q^{39} - 960 q^{40} - 414 q^{41} - 486 q^{42} - 418 q^{43} - 474 q^{44} - 462 q^{45} - 426 q^{46} - 438 q^{47} - 534 q^{48} - 433 q^{49} - 471 q^{50} - 438 q^{51} - 440 q^{52} - 900 q^{53} - 534 q^{54} - 462 q^{55} - 510 q^{56} - 470 q^{57} - 498 q^{58} - 474 q^{59} - 558 q^{60} - 450 q^{61} - 498 q^{62} - 390 q^{63} - 201 q^{64} - 339 q^{65} - 690 q^{66} - 288 q^{67} - 198 q^{68} - 198 q^{69} + 90 q^{70} - 318 q^{71} + 189 q^{72} - 308 q^{73} - 162 q^{74} - 194 q^{75} + 210 q^{76} - 252 q^{77} - 198 q^{78} - 477 q^{79} - 156 q^{80} - 65 q^{81} - 222 q^{82} - 240 q^{83} + 114 q^{84} - 204 q^{85} - 210 q^{86} - 342 q^{87} + 210 q^{88} - 300 q^{89} - 12 q^{90} - 281 q^{91} - 738 q^{92} - 312 q^{93} - 210 q^{94} - 366 q^{95} - 330 q^{96} - 408 q^{97} - 603 q^{98} - 546 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1027))\)

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
1027.2.a \(\chi_{1027}(1, \cdot)\) 1027.2.a.a 1 1
1027.2.a.b 17
1027.2.a.c 18
1027.2.a.d 21
1027.2.a.e 22
1027.2.c \(\chi_{1027}(870, \cdot)\) 1027.2.c.a 2 1
1027.2.c.b 40
1027.2.c.c 48
1027.2.e \(\chi_{1027}(497, \cdot)\) n/a 182 2
1027.2.f \(\chi_{1027}(339, \cdot)\) n/a 160 2
1027.2.g \(\chi_{1027}(159, \cdot)\) n/a 184 2
1027.2.h \(\chi_{1027}(55, \cdot)\) n/a 182 2
1027.2.i \(\chi_{1027}(473, \cdot)\) n/a 180 2
1027.2.l \(\chi_{1027}(576, \cdot)\) n/a 182 2
1027.2.p \(\chi_{1027}(238, \cdot)\) n/a 180 2
1027.2.q \(\chi_{1027}(23, \cdot)\) n/a 182 2
1027.2.r \(\chi_{1027}(181, \cdot)\) n/a 184 2
1027.2.w \(\chi_{1027}(24, \cdot)\) n/a 364 4
1027.2.ba \(\chi_{1027}(135, \cdot)\) n/a 368 4
1027.2.bb \(\chi_{1027}(609, \cdot)\) n/a 364 4
1027.2.bc \(\chi_{1027}(236, \cdot)\) n/a 368 4
1027.2.be \(\chi_{1027}(131, \cdot)\) n/a 960 12
1027.2.bg \(\chi_{1027}(38, \cdot)\) n/a 1080 12
1027.2.bi \(\chi_{1027}(9, \cdot)\) n/a 2184 24
1027.2.bj \(\chi_{1027}(22, \cdot)\) n/a 2208 24
1027.2.bk \(\chi_{1027}(40, \cdot)\) n/a 1920 24
1027.2.bl \(\chi_{1027}(178, \cdot)\) n/a 2184 24
1027.2.bn \(\chi_{1027}(57, \cdot)\) n/a 2160 24
1027.2.bs \(\chi_{1027}(25, \cdot)\) n/a 2208 24
1027.2.bt \(\chi_{1027}(88, \cdot)\) n/a 2184 24
1027.2.bu \(\chi_{1027}(10, \cdot)\) n/a 2208 24
1027.2.by \(\chi_{1027}(4, \cdot)\) n/a 2184 24
1027.2.cb \(\chi_{1027}(59, \cdot)\) n/a 4368 48
1027.2.cc \(\chi_{1027}(15, \cdot)\) n/a 4416 48
1027.2.cd \(\chi_{1027}(34, \cdot)\) n/a 4416 48
1027.2.ch \(\chi_{1027}(6, \cdot)\) n/a 4368 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1027))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1027)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1027))\)\(^{\oplus 1}\)