Properties

Label 1421.2
Level 1421
Weight 2
Dimension 77499
Nonzero newspaces 54
Sturm bound 329280
Trace bound 12

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Defining parameters

Level: \( N \) = \( 1421 = 7^{2} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 54 \)
Sturm bound: \(329280\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1421))\).

Total New Old
Modular forms 84000 80117 3883
Cusp forms 80641 77499 3142
Eisenstein series 3359 2618 741

Trace form

\( 77499 q - 398 q^{2} - 400 q^{3} - 406 q^{4} - 404 q^{5} - 416 q^{6} - 476 q^{7} - 722 q^{8} - 418 q^{9} + O(q^{10}) \) \( 77499 q - 398 q^{2} - 400 q^{3} - 406 q^{4} - 404 q^{5} - 416 q^{6} - 476 q^{7} - 722 q^{8} - 418 q^{9} - 428 q^{10} - 416 q^{11} - 448 q^{12} - 420 q^{13} - 504 q^{14} - 740 q^{15} - 454 q^{16} - 428 q^{17} - 470 q^{18} - 432 q^{19} - 497 q^{20} - 518 q^{21} - 792 q^{22} - 454 q^{23} - 596 q^{24} - 482 q^{25} - 511 q^{26} - 514 q^{27} - 560 q^{28} - 789 q^{29} - 1054 q^{30} - 484 q^{31} - 574 q^{32} - 530 q^{33} - 535 q^{34} - 546 q^{35} - 850 q^{36} - 426 q^{37} - 456 q^{38} - 434 q^{39} - 341 q^{40} - 392 q^{41} - 462 q^{42} - 696 q^{43} - 322 q^{44} - 373 q^{45} - 354 q^{46} - 432 q^{47} - 402 q^{48} - 392 q^{49} - 1354 q^{50} - 424 q^{51} - 392 q^{52} - 479 q^{53} - 506 q^{54} - 438 q^{55} - 420 q^{56} - 838 q^{57} - 587 q^{58} - 890 q^{59} - 672 q^{60} - 474 q^{61} - 598 q^{62} - 588 q^{63} - 928 q^{64} - 623 q^{65} - 792 q^{66} - 584 q^{67} - 742 q^{68} - 640 q^{69} - 714 q^{70} - 906 q^{71} - 936 q^{72} - 603 q^{73} - 718 q^{74} - 710 q^{75} - 784 q^{76} - 630 q^{77} - 924 q^{78} - 580 q^{79} - 834 q^{80} - 578 q^{81} - 490 q^{82} - 448 q^{83} - 392 q^{84} - 824 q^{85} - 516 q^{86} - 435 q^{87} - 892 q^{88} - 474 q^{89} - 244 q^{90} - 490 q^{91} - 902 q^{92} - 200 q^{93} - 358 q^{94} - 408 q^{95} - 336 q^{96} - 455 q^{97} - 168 q^{98} - 1396 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1421))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
1421.2.a \(\chi_{1421}(1, \cdot)\) 1421.2.a.a 1 1
1421.2.a.b 1
1421.2.a.c 1
1421.2.a.d 1
1421.2.a.e 1
1421.2.a.f 1
1421.2.a.g 1
1421.2.a.h 1
1421.2.a.i 1
1421.2.a.j 2
1421.2.a.k 2
1421.2.a.l 2
1421.2.a.m 2
1421.2.a.n 3
1421.2.a.o 4
1421.2.a.p 4
1421.2.a.q 5
1421.2.a.r 8
1421.2.a.s 8
1421.2.a.t 8
1421.2.a.u 8
1421.2.a.v 10
1421.2.a.w 20
1421.2.b \(\chi_{1421}(1275, \cdot)\) 1421.2.b.a 2 1
1421.2.b.b 2
1421.2.b.c 2
1421.2.b.d 4
1421.2.b.e 4
1421.2.b.f 4
1421.2.b.g 6
1421.2.b.h 6
1421.2.b.i 12
1421.2.b.j 18
1421.2.b.k 18
1421.2.b.l 20
1421.2.e \(\chi_{1421}(30, \cdot)\) n/a 188 2
1421.2.g \(\chi_{1421}(244, \cdot)\) n/a 192 2
1421.2.j \(\chi_{1421}(753, \cdot)\) n/a 192 2
1421.2.k \(\chi_{1421}(239, \cdot)\) n/a 828 6
1421.2.l \(\chi_{1421}(36, \cdot)\) n/a 828 6
1421.2.m \(\chi_{1421}(190, \cdot)\) n/a 828 6
1421.2.n \(\chi_{1421}(204, \cdot)\) n/a 792 6
1421.2.o \(\chi_{1421}(197, \cdot)\) n/a 582 6
1421.2.p \(\chi_{1421}(484, \cdot)\) n/a 828 6
1421.2.q \(\chi_{1421}(141, \cdot)\) n/a 828 6
1421.2.r \(\chi_{1421}(78, \cdot)\) n/a 828 6
1421.2.s \(\chi_{1421}(215, \cdot)\) n/a 384 4
1421.2.v \(\chi_{1421}(71, \cdot)\) n/a 828 6
1421.2.bd \(\chi_{1421}(470, \cdot)\) n/a 828 6
1421.2.bk \(\chi_{1421}(295, \cdot)\) n/a 588 6
1421.2.bl \(\chi_{1421}(57, \cdot)\) n/a 828 6
1421.2.bm \(\chi_{1421}(183, \cdot)\) n/a 828 6
1421.2.bn \(\chi_{1421}(274, \cdot)\) n/a 828 6
1421.2.bo \(\chi_{1421}(64, \cdot)\) n/a 828 6
1421.2.bp \(\chi_{1421}(22, \cdot)\) n/a 828 6
1421.2.bs \(\chi_{1421}(123, \cdot)\) n/a 1656 12
1421.2.bt \(\chi_{1421}(53, \cdot)\) n/a 1656 12
1421.2.bu \(\chi_{1421}(228, \cdot)\) n/a 1656 12
1421.2.bv \(\chi_{1421}(165, \cdot)\) n/a 1152 12
1421.2.bw \(\chi_{1421}(88, \cdot)\) n/a 1560 12
1421.2.bx \(\chi_{1421}(23, \cdot)\) n/a 1656 12
1421.2.by \(\chi_{1421}(25, \cdot)\) n/a 1656 12
1421.2.bz \(\chi_{1421}(16, \cdot)\) n/a 1656 12
1421.2.ca \(\chi_{1421}(76, \cdot)\) n/a 1656 12
1421.2.cd \(\chi_{1421}(27, \cdot)\) n/a 1656 12
1421.2.ce \(\chi_{1421}(461, \cdot)\) n/a 1656 12
1421.2.cf \(\chi_{1421}(69, \cdot)\) n/a 1656 12
1421.2.cg \(\chi_{1421}(48, \cdot)\) n/a 1152 12
1421.2.ch \(\chi_{1421}(41, \cdot)\) n/a 1656 12
1421.2.ci \(\chi_{1421}(55, \cdot)\) n/a 1656 12
1421.2.cp \(\chi_{1421}(153, \cdot)\) n/a 1656 12
1421.2.cs \(\chi_{1421}(212, \cdot)\) n/a 1656 12
1421.2.ct \(\chi_{1421}(151, \cdot)\) n/a 1656 12
1421.2.cu \(\chi_{1421}(51, \cdot)\) n/a 1656 12
1421.2.cv \(\chi_{1421}(4, \cdot)\) n/a 1656 12
1421.2.cw \(\chi_{1421}(86, \cdot)\) n/a 1656 12
1421.2.cx \(\chi_{1421}(67, \cdot)\) n/a 1152 12
1421.2.de \(\chi_{1421}(9, \cdot)\) n/a 1656 12
1421.2.dm \(\chi_{1421}(93, \cdot)\) n/a 1656 12
1421.2.do \(\chi_{1421}(26, \cdot)\) n/a 3312 24
1421.2.dv \(\chi_{1421}(61, \cdot)\) n/a 3312 24
1421.2.dw \(\chi_{1421}(124, \cdot)\) n/a 3312 24
1421.2.dx \(\chi_{1421}(40, \cdot)\) n/a 3312 24
1421.2.dy \(\chi_{1421}(19, \cdot)\) n/a 2304 24
1421.2.dz \(\chi_{1421}(12, \cdot)\) n/a 3312 24
1421.2.ea \(\chi_{1421}(3, \cdot)\) n/a 3312 24
1421.2.ed \(\chi_{1421}(66, \cdot)\) n/a 3312 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1421))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1421)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(203))\)\(^{\oplus 2}\)