Properties

Label 1421.4
Level 1421
Weight 4
Dimension 235111
Nonzero newspaces 54
Sturm bound 658560
Trace bound 12

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Defining parameters

Level: \( N \) = \( 1421 = 7^{2} \cdot 29 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 54 \)
Sturm bound: \(658560\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1421))\).

Total New Old
Modular forms 248640 237729 10911
Cusp forms 245280 235111 10169
Eisenstein series 3360 2618 742

Trace form

\( 235111 q - 404 q^{2} - 428 q^{3} - 404 q^{4} - 356 q^{5} - 272 q^{6} - 420 q^{7} - 824 q^{8} - 572 q^{9} + O(q^{10}) \) \( 235111 q - 404 q^{2} - 428 q^{3} - 404 q^{4} - 356 q^{5} - 272 q^{6} - 420 q^{7} - 824 q^{8} - 572 q^{9} - 512 q^{10} - 404 q^{11} - 224 q^{12} - 392 q^{13} - 420 q^{14} - 428 q^{15} - 164 q^{16} - 92 q^{17} - 476 q^{18} - 1028 q^{19} - 1988 q^{20} - 924 q^{21} - 1132 q^{22} + 408 q^{23} + 832 q^{24} + 884 q^{25} + 378 q^{26} + 820 q^{27} - 84 q^{28} + 65 q^{29} + 1094 q^{30} - 316 q^{31} - 780 q^{32} + 148 q^{33} - 1014 q^{34} - 588 q^{35} + 784 q^{36} + 1836 q^{37} + 3128 q^{38} + 1596 q^{39} + 5104 q^{40} + 3808 q^{41} - 714 q^{42} - 2684 q^{43} - 9054 q^{44} - 13505 q^{45} - 15146 q^{46} - 6544 q^{47} - 20054 q^{48} - 8232 q^{49} - 10608 q^{50} - 6452 q^{51} - 9464 q^{52} - 2273 q^{53} + 622 q^{54} + 3268 q^{55} + 8126 q^{57} + 12679 q^{58} + 9582 q^{59} + 30912 q^{60} + 12412 q^{61} + 16794 q^{62} + 9240 q^{63} + 13330 q^{64} + 1855 q^{65} - 1856 q^{66} - 2924 q^{67} - 7434 q^{68} - 13880 q^{69} - 1218 q^{70} - 17188 q^{71} - 20786 q^{72} - 7841 q^{73} - 10050 q^{74} - 2532 q^{75} - 1568 q^{76} + 7308 q^{78} + 2620 q^{79} + 37638 q^{80} + 40320 q^{81} + 29806 q^{82} + 26264 q^{83} + 38220 q^{84} + 18556 q^{85} + 22404 q^{86} + 7419 q^{87} + 9092 q^{88} + 5244 q^{89} - 19192 q^{90} - 10878 q^{91} - 7238 q^{92} - 40948 q^{93} - 36338 q^{94} - 37812 q^{95} - 82992 q^{96} - 34321 q^{97} - 55440 q^{98} - 55786 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1421))\)

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
1421.4.a \(\chi_{1421}(1, \cdot)\) 1421.4.a.a 1 1
1421.4.a.b 1
1421.4.a.c 2
1421.4.a.d 2
1421.4.a.e 5
1421.4.a.f 7
1421.4.a.g 10
1421.4.a.h 11
1421.4.a.i 12
1421.4.a.j 18
1421.4.a.k 24
1421.4.a.l 28
1421.4.a.m 28
1421.4.a.n 28
1421.4.a.o 28
1421.4.a.p 34
1421.4.a.q 48
1421.4.b \(\chi_{1421}(1275, \cdot)\) n/a 302 1
1421.4.e \(\chi_{1421}(30, \cdot)\) n/a 560 2
1421.4.g \(\chi_{1421}(244, \cdot)\) n/a 592 2
1421.4.j \(\chi_{1421}(753, \cdot)\) n/a 592 2
1421.4.k \(\chi_{1421}(239, \cdot)\) n/a 2508 6
1421.4.l \(\chi_{1421}(36, \cdot)\) n/a 2508 6
1421.4.m \(\chi_{1421}(190, \cdot)\) n/a 2508 6
1421.4.n \(\chi_{1421}(204, \cdot)\) n/a 2352 6
1421.4.o \(\chi_{1421}(197, \cdot)\) n/a 1818 6
1421.4.p \(\chi_{1421}(484, \cdot)\) n/a 2508 6
1421.4.q \(\chi_{1421}(141, \cdot)\) n/a 2508 6
1421.4.r \(\chi_{1421}(78, \cdot)\) n/a 2508 6
1421.4.s \(\chi_{1421}(215, \cdot)\) n/a 1184 4
1421.4.v \(\chi_{1421}(71, \cdot)\) n/a 2508 6
1421.4.bd \(\chi_{1421}(470, \cdot)\) n/a 2508 6
1421.4.bk \(\chi_{1421}(295, \cdot)\) n/a 1812 6
1421.4.bl \(\chi_{1421}(57, \cdot)\) n/a 2508 6
1421.4.bm \(\chi_{1421}(183, \cdot)\) n/a 2508 6
1421.4.bn \(\chi_{1421}(274, \cdot)\) n/a 2508 6
1421.4.bo \(\chi_{1421}(64, \cdot)\) n/a 2508 6
1421.4.bp \(\chi_{1421}(22, \cdot)\) n/a 2508 6
1421.4.bs \(\chi_{1421}(123, \cdot)\) n/a 5016 12
1421.4.bt \(\chi_{1421}(53, \cdot)\) n/a 5016 12
1421.4.bu \(\chi_{1421}(228, \cdot)\) n/a 5016 12
1421.4.bv \(\chi_{1421}(165, \cdot)\) n/a 3552 12
1421.4.bw \(\chi_{1421}(88, \cdot)\) n/a 4704 12
1421.4.bx \(\chi_{1421}(23, \cdot)\) n/a 5016 12
1421.4.by \(\chi_{1421}(25, \cdot)\) n/a 5016 12
1421.4.bz \(\chi_{1421}(16, \cdot)\) n/a 5016 12
1421.4.ca \(\chi_{1421}(76, \cdot)\) n/a 5016 12
1421.4.cd \(\chi_{1421}(27, \cdot)\) n/a 5016 12
1421.4.ce \(\chi_{1421}(461, \cdot)\) n/a 5016 12
1421.4.cf \(\chi_{1421}(69, \cdot)\) n/a 5016 12
1421.4.cg \(\chi_{1421}(48, \cdot)\) n/a 3552 12
1421.4.ch \(\chi_{1421}(41, \cdot)\) n/a 5016 12
1421.4.ci \(\chi_{1421}(55, \cdot)\) n/a 5016 12
1421.4.cp \(\chi_{1421}(153, \cdot)\) n/a 5016 12
1421.4.cs \(\chi_{1421}(212, \cdot)\) n/a 5016 12
1421.4.ct \(\chi_{1421}(151, \cdot)\) n/a 5016 12
1421.4.cu \(\chi_{1421}(51, \cdot)\) n/a 5016 12
1421.4.cv \(\chi_{1421}(4, \cdot)\) n/a 5016 12
1421.4.cw \(\chi_{1421}(86, \cdot)\) n/a 5016 12
1421.4.cx \(\chi_{1421}(67, \cdot)\) n/a 3552 12
1421.4.de \(\chi_{1421}(9, \cdot)\) n/a 5016 12
1421.4.dm \(\chi_{1421}(93, \cdot)\) n/a 5016 12
1421.4.do \(\chi_{1421}(26, \cdot)\) n/a 10032 24
1421.4.dv \(\chi_{1421}(61, \cdot)\) n/a 10032 24
1421.4.dw \(\chi_{1421}(124, \cdot)\) n/a 10032 24
1421.4.dx \(\chi_{1421}(40, \cdot)\) n/a 10032 24
1421.4.dy \(\chi_{1421}(19, \cdot)\) n/a 7104 24
1421.4.dz \(\chi_{1421}(12, \cdot)\) n/a 10032 24
1421.4.ea \(\chi_{1421}(3, \cdot)\) n/a 10032 24
1421.4.ed \(\chi_{1421}(66, \cdot)\) n/a 10032 24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1421))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1421)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(203))\)\(^{\oplus 2}\)