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Properties

Label 1247.2
Level 1247
Weight 2
Dimension 63347
Nonzero newspaces 54
Sturm bound 258720
Trace bound 8

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Defining parameters

Level: \( N \) = \( 1247 = 29 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 54 \)
Sturm bound: \(258720\)
Trace bound: \(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1247))\).

Total New Old
Modular forms 65856 65563 293
Cusp forms 63505 63347 158
Eisenstein series 2351 2216 135

Trace form

\( 63347 q - 527 q^{2} - 530 q^{3} - 539 q^{4} - 536 q^{5} - 554 q^{6} - 542 q^{7} - 563 q^{8} - 557 q^{9} + O(q^{10}) \) \( 63347 q - 527 q^{2} - 530 q^{3} - 539 q^{4} - 536 q^{5} - 554 q^{6} - 542 q^{7} - 563 q^{8} - 557 q^{9} - 572 q^{10} - 554 q^{11} - 602 q^{12} - 560 q^{13} - 590 q^{14} - 590 q^{15} - 611 q^{16} - 572 q^{17} - 635 q^{18} - 578 q^{19} - 602 q^{20} - 558 q^{21} - 570 q^{22} - 562 q^{23} - 530 q^{24} - 555 q^{25} - 574 q^{26} - 554 q^{27} - 546 q^{28} - 542 q^{29} - 1126 q^{30} - 544 q^{31} - 511 q^{32} - 494 q^{33} - 484 q^{34} - 522 q^{35} - 399 q^{36} - 520 q^{37} - 474 q^{38} - 532 q^{39} - 410 q^{40} - 602 q^{41} - 596 q^{42} - 409 q^{43} - 1120 q^{44} - 472 q^{45} - 426 q^{46} - 564 q^{47} - 330 q^{48} - 479 q^{49} - 433 q^{50} - 538 q^{51} - 364 q^{52} - 470 q^{53} - 500 q^{54} - 426 q^{55} - 542 q^{56} - 604 q^{57} - 380 q^{58} - 1202 q^{59} - 630 q^{60} - 592 q^{61} - 610 q^{62} - 606 q^{63} - 647 q^{64} - 644 q^{65} - 726 q^{66} - 610 q^{67} - 700 q^{68} - 610 q^{69} - 502 q^{70} - 510 q^{71} - 375 q^{72} - 530 q^{73} - 370 q^{74} - 456 q^{75} - 420 q^{76} - 414 q^{77} - 252 q^{78} - 534 q^{79} - 348 q^{80} - 321 q^{81} - 364 q^{82} - 490 q^{83} + 70 q^{84} - 464 q^{85} - 303 q^{86} - 992 q^{87} - 862 q^{88} - 480 q^{89} - 100 q^{90} - 518 q^{91} - 266 q^{92} - 454 q^{93} - 502 q^{94} - 486 q^{95} - 252 q^{96} - 406 q^{97} - 373 q^{98} - 328 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1247))\)

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
1247.2.a \(\chi_{1247}(1, \cdot)\) 1247.2.a.a 18 1
1247.2.a.b 19
1247.2.a.c 30
1247.2.a.d 32
1247.2.c \(\chi_{1247}(173, \cdot)\) n/a 104 1
1247.2.e \(\chi_{1247}(436, \cdot)\) n/a 204 2
1247.2.g \(\chi_{1247}(128, \cdot)\) n/a 216 2
1247.2.h \(\chi_{1247}(608, \cdot)\) n/a 216 2
1247.2.k \(\chi_{1247}(54, \cdot)\) n/a 648 6
1247.2.l \(\chi_{1247}(140, \cdot)\) n/a 648 6
1247.2.m \(\chi_{1247}(431, \cdot)\) n/a 636 6
1247.2.n \(\chi_{1247}(16, \cdot)\) n/a 648 6
1247.2.o \(\chi_{1247}(59, \cdot)\) n/a 624 6
1247.2.p \(\chi_{1247}(471, \cdot)\) n/a 648 6
1247.2.q \(\chi_{1247}(170, \cdot)\) n/a 648 6
1247.2.r \(\chi_{1247}(107, \cdot)\) n/a 648 6
1247.2.s \(\chi_{1247}(394, \cdot)\) n/a 432 4
1247.2.u \(\chi_{1247}(441, \cdot)\) n/a 648 6
1247.2.bd \(\chi_{1247}(35, \cdot)\) n/a 648 6
1247.2.bg \(\chi_{1247}(4, \cdot)\) n/a 648 6
1247.2.bh \(\chi_{1247}(216, \cdot)\) n/a 624 6
1247.2.bi \(\chi_{1247}(150, \cdot)\) n/a 648 6
1247.2.bj \(\chi_{1247}(207, \cdot)\) n/a 648 6
1247.2.bk \(\chi_{1247}(231, \cdot)\) n/a 648 6
1247.2.bq \(\chi_{1247}(121, \cdot)\) n/a 648 6
1247.2.bs \(\chi_{1247}(53, \cdot)\) n/a 1296 12
1247.2.bt \(\chi_{1247}(25, \cdot)\) n/a 1296 12
1247.2.bu \(\chi_{1247}(117, \cdot)\) n/a 1224 12
1247.2.bv \(\chi_{1247}(103, \cdot)\) n/a 1296 12
1247.2.bw \(\chi_{1247}(36, \cdot)\) n/a 1296 12
1247.2.bx \(\chi_{1247}(110, \cdot)\) n/a 1296 12
1247.2.by \(\chi_{1247}(111, \cdot)\) n/a 1296 12
1247.2.bz \(\chi_{1247}(23, \cdot)\) n/a 1296 12
1247.2.ca \(\chi_{1247}(108, \cdot)\) n/a 1296 12
1247.2.cd \(\chi_{1247}(70, \cdot)\) n/a 1296 12
1247.2.ce \(\chi_{1247}(27, \cdot)\) n/a 1296 12
1247.2.cf \(\chi_{1247}(113, \cdot)\) n/a 1296 12
1247.2.cg \(\chi_{1247}(131, \cdot)\) n/a 1296 12
1247.2.ch \(\chi_{1247}(85, \cdot)\) n/a 1296 12
1247.2.ci \(\chi_{1247}(2, \cdot)\) n/a 1296 12
1247.2.cp \(\chi_{1247}(211, \cdot)\) n/a 1296 12
1247.2.cr \(\chi_{1247}(100, \cdot)\) n/a 1296 12
1247.2.cz \(\chi_{1247}(67, \cdot)\) n/a 1296 12
1247.2.df \(\chi_{1247}(57, \cdot)\) n/a 1296 12
1247.2.dg \(\chi_{1247}(225, \cdot)\) n/a 1296 12
1247.2.dh \(\chi_{1247}(13, \cdot)\) n/a 1296 12
1247.2.di \(\chi_{1247}(6, \cdot)\) n/a 1296 12
1247.2.dj \(\chi_{1247}(38, \cdot)\) n/a 1296 12
1247.2.dm \(\chi_{1247}(9, \cdot)\) n/a 1296 12
1247.2.dp \(\chi_{1247}(98, \cdot)\) n/a 2592 24
1247.2.dq \(\chi_{1247}(55, \cdot)\) n/a 2592 24
1247.2.dx \(\chi_{1247}(19, \cdot)\) n/a 2592 24
1247.2.dy \(\chi_{1247}(37, \cdot)\) n/a 2592 24
1247.2.dz \(\chi_{1247}(72, \cdot)\) n/a 2592 24
1247.2.ea \(\chi_{1247}(18, \cdot)\) n/a 2592 24
1247.2.eb \(\chi_{1247}(3, \cdot)\) n/a 2592 24
1247.2.ec \(\chi_{1247}(12, \cdot)\) n/a 2592 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1247))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1247)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(43))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1247))\)\(^{\oplus 1}\)