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Properties

Label 1127.2
Level 1127
Weight 2
Dimension 48449
Nonzero newspaces 16
Sturm bound 206976
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1127 = 7^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(206976\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1127))\).

Total New Old
Modular forms 53064 50485 2579
Cusp forms 50425 48449 1976
Eisenstein series 2639 2036 603

Trace form

\( 48449 q - 305 q^{2} - 307 q^{3} - 313 q^{4} - 311 q^{5} - 323 q^{6} - 368 q^{7} - 557 q^{8} - 325 q^{9} + O(q^{10}) \) \( 48449 q - 305 q^{2} - 307 q^{3} - 313 q^{4} - 311 q^{5} - 323 q^{6} - 368 q^{7} - 557 q^{8} - 325 q^{9} - 335 q^{10} - 323 q^{11} - 355 q^{12} - 327 q^{13} - 396 q^{14} - 586 q^{15} - 383 q^{16} - 346 q^{17} - 421 q^{18} - 350 q^{19} - 427 q^{20} - 410 q^{21} - 632 q^{22} - 366 q^{23} - 826 q^{24} - 383 q^{25} - 405 q^{26} - 412 q^{27} - 452 q^{28} - 598 q^{29} - 487 q^{30} - 374 q^{31} - 447 q^{32} - 406 q^{33} - 429 q^{34} - 438 q^{35} - 656 q^{36} - 363 q^{37} - 390 q^{38} - 357 q^{39} - 315 q^{40} - 321 q^{41} - 354 q^{42} - 575 q^{43} - 314 q^{44} - 322 q^{45} - 354 q^{46} - 696 q^{47} - 307 q^{48} - 284 q^{49} - 1042 q^{50} - 319 q^{51} - 297 q^{52} - 345 q^{53} - 397 q^{54} - 299 q^{55} - 312 q^{56} - 680 q^{57} - 410 q^{58} - 401 q^{59} - 515 q^{60} - 369 q^{61} - 473 q^{62} - 480 q^{63} - 725 q^{64} - 544 q^{65} - 708 q^{66} - 457 q^{67} - 694 q^{68} - 471 q^{69} - 1002 q^{70} - 726 q^{71} - 854 q^{72} - 469 q^{73} - 626 q^{74} - 668 q^{75} - 722 q^{76} - 522 q^{77} - 823 q^{78} - 547 q^{79} - 754 q^{80} - 549 q^{81} - 451 q^{82} - 376 q^{83} - 284 q^{84} - 707 q^{85} - 401 q^{86} - 335 q^{87} - 329 q^{88} - 377 q^{89} - 200 q^{90} - 382 q^{91} - 686 q^{92} - 524 q^{93} - 330 q^{94} - 302 q^{95} - 302 q^{96} - 384 q^{97} - 60 q^{98} - 1110 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1127))\)

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
1127.2.a \(\chi_{1127}(1, \cdot)\) 1127.2.a.a 1 1
1127.2.a.b 2
1127.2.a.c 2
1127.2.a.d 2
1127.2.a.e 2
1127.2.a.f 3
1127.2.a.g 4
1127.2.a.h 5
1127.2.a.i 6
1127.2.a.j 6
1127.2.a.k 7
1127.2.a.l 7
1127.2.a.m 7
1127.2.a.n 7
1127.2.a.o 14
1127.2.c \(\chi_{1127}(1126, \cdot)\) 1127.2.c.a 24 1
1127.2.c.b 24
1127.2.c.c 28
1127.2.e \(\chi_{1127}(116, \cdot)\) n/a 148 2
1127.2.g \(\chi_{1127}(68, \cdot)\) n/a 152 2
1127.2.i \(\chi_{1127}(162, \cdot)\) n/a 624 6
1127.2.j \(\chi_{1127}(50, \cdot)\) n/a 770 10
1127.2.l \(\chi_{1127}(160, \cdot)\) n/a 660 6
1127.2.n \(\chi_{1127}(93, \cdot)\) n/a 1224 12
1127.2.p \(\chi_{1127}(97, \cdot)\) n/a 760 10
1127.2.r \(\chi_{1127}(18, \cdot)\) n/a 1520 20
1127.2.t \(\chi_{1127}(45, \cdot)\) n/a 1320 12
1127.2.w \(\chi_{1127}(19, \cdot)\) n/a 1520 20
1127.2.y \(\chi_{1127}(8, \cdot)\) n/a 6600 60
1127.2.ba \(\chi_{1127}(20, \cdot)\) n/a 6600 60
1127.2.bc \(\chi_{1127}(2, \cdot)\) n/a 13200 120
1127.2.be \(\chi_{1127}(5, \cdot)\) n/a 13200 120

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1127))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1127)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(161))\)\(^{\oplus 2}\)