Properties

Label 1840.4
Level 1840
Weight 4
Dimension 155654
Nonzero newspaces 28
Sturm bound 811008
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(811008\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1840))\).

Total New Old
Modular forms 306592 156790 149802
Cusp forms 301664 155654 146010
Eisenstein series 4928 1136 3792

Trace form

\( 155654 q - 80 q^{2} - 46 q^{3} - 40 q^{4} - 153 q^{5} - 360 q^{6} - 150 q^{7} - 248 q^{8} - 58 q^{9} + O(q^{10}) \) \( 155654 q - 80 q^{2} - 46 q^{3} - 40 q^{4} - 153 q^{5} - 360 q^{6} - 150 q^{7} - 248 q^{8} - 58 q^{9} - 252 q^{10} + 74 q^{11} + 328 q^{12} + 174 q^{13} + 680 q^{14} - 327 q^{15} + 888 q^{16} - 186 q^{17} + 624 q^{18} - 794 q^{19} - 508 q^{20} - 1010 q^{21} - 2424 q^{22} - 32 q^{23} - 3552 q^{24} - 345 q^{25} - 1288 q^{26} + 854 q^{27} + 24 q^{28} - 670 q^{29} - 908 q^{30} + 1410 q^{31} + 2440 q^{32} + 442 q^{33} + 2824 q^{34} + 1417 q^{35} + 840 q^{36} + 1862 q^{37} - 856 q^{38} + 1526 q^{39} + 3452 q^{40} + 1518 q^{41} + 2488 q^{42} - 2750 q^{43} + 5528 q^{44} + 1518 q^{45} + 1824 q^{46} - 4088 q^{47} + 2776 q^{48} - 482 q^{49} - 3844 q^{50} - 6238 q^{51} - 8504 q^{52} - 5674 q^{53} - 9032 q^{54} - 2635 q^{55} - 2184 q^{56} - 4006 q^{57} - 40 q^{58} + 5190 q^{59} + 524 q^{60} + 3726 q^{61} - 392 q^{62} + 1162 q^{63} + 9704 q^{64} - 4237 q^{65} + 11240 q^{66} - 2422 q^{67} + 2344 q^{68} + 1510 q^{69} + 1656 q^{70} + 1538 q^{71} - 1224 q^{72} + 4238 q^{73} - 10504 q^{74} + 25347 q^{75} - 13720 q^{76} + 9962 q^{77} - 26696 q^{78} + 9298 q^{79} - 18052 q^{80} + 12230 q^{81} - 14696 q^{82} + 3798 q^{83} - 10168 q^{84} - 45 q^{85} + 10088 q^{86} - 15934 q^{87} + 4808 q^{88} - 11678 q^{89} + 11116 q^{90} - 24076 q^{91} + 6216 q^{92} - 38388 q^{93} + 1608 q^{94} - 20151 q^{95} + 6744 q^{96} - 20594 q^{97} + 8320 q^{98} - 20646 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1840))\)

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
1840.4.a \(\chi_{1840}(1, \cdot)\) 1840.4.a.a 1 1
1840.4.a.b 1
1840.4.a.c 1
1840.4.a.d 1
1840.4.a.e 1
1840.4.a.f 1
1840.4.a.g 1
1840.4.a.h 2
1840.4.a.i 2
1840.4.a.j 3
1840.4.a.k 4
1840.4.a.l 4
1840.4.a.m 4
1840.4.a.n 5
1840.4.a.o 5
1840.4.a.p 5
1840.4.a.q 5
1840.4.a.r 6
1840.4.a.s 6
1840.4.a.t 6
1840.4.a.u 6
1840.4.a.v 8
1840.4.a.w 8
1840.4.a.x 8
1840.4.a.y 9
1840.4.a.z 9
1840.4.a.ba 10
1840.4.a.bb 10
1840.4.b \(\chi_{1840}(919, \cdot)\) None 0 1
1840.4.e \(\chi_{1840}(369, \cdot)\) n/a 198 1
1840.4.f \(\chi_{1840}(921, \cdot)\) None 0 1
1840.4.i \(\chi_{1840}(1471, \cdot)\) n/a 144 1
1840.4.j \(\chi_{1840}(1289, \cdot)\) None 0 1
1840.4.m \(\chi_{1840}(1839, \cdot)\) n/a 216 1
1840.4.n \(\chi_{1840}(551, \cdot)\) None 0 1
1840.4.r \(\chi_{1840}(413, \cdot)\) n/a 1720 2
1840.4.t \(\chi_{1840}(1243, \cdot)\) n/a 1584 2
1840.4.u \(\chi_{1840}(91, \cdot)\) n/a 1152 2
1840.4.x \(\chi_{1840}(461, \cdot)\) n/a 1056 2
1840.4.y \(\chi_{1840}(1057, \cdot)\) n/a 428 2
1840.4.ba \(\chi_{1840}(47, \cdot)\) n/a 396 2
1840.4.bd \(\chi_{1840}(967, \cdot)\) None 0 2
1840.4.bf \(\chi_{1840}(137, \cdot)\) None 0 2
1840.4.bg \(\chi_{1840}(829, \cdot)\) n/a 1584 2
1840.4.bj \(\chi_{1840}(459, \cdot)\) n/a 1720 2
1840.4.bk \(\chi_{1840}(323, \cdot)\) n/a 1584 2
1840.4.bm \(\chi_{1840}(1333, \cdot)\) n/a 1720 2
1840.4.bo \(\chi_{1840}(81, \cdot)\) n/a 1440 10
1840.4.br \(\chi_{1840}(471, \cdot)\) None 0 10
1840.4.bs \(\chi_{1840}(79, \cdot)\) n/a 2160 10
1840.4.bv \(\chi_{1840}(9, \cdot)\) None 0 10
1840.4.bw \(\chi_{1840}(111, \cdot)\) n/a 1440 10
1840.4.bz \(\chi_{1840}(41, \cdot)\) None 0 10
1840.4.ca \(\chi_{1840}(49, \cdot)\) n/a 2140 10
1840.4.cd \(\chi_{1840}(199, \cdot)\) None 0 10
1840.4.cf \(\chi_{1840}(53, \cdot)\) n/a 17200 20
1840.4.ch \(\chi_{1840}(3, \cdot)\) n/a 17200 20
1840.4.cj \(\chi_{1840}(19, \cdot)\) n/a 17200 20
1840.4.ck \(\chi_{1840}(29, \cdot)\) n/a 17200 20
1840.4.cm \(\chi_{1840}(57, \cdot)\) None 0 20
1840.4.co \(\chi_{1840}(87, \cdot)\) None 0 20
1840.4.cr \(\chi_{1840}(127, \cdot)\) n/a 4320 20
1840.4.ct \(\chi_{1840}(17, \cdot)\) n/a 4280 20
1840.4.cv \(\chi_{1840}(101, \cdot)\) n/a 11520 20
1840.4.cw \(\chi_{1840}(11, \cdot)\) n/a 11520 20
1840.4.cy \(\chi_{1840}(123, \cdot)\) n/a 17200 20
1840.4.da \(\chi_{1840}(37, \cdot)\) n/a 17200 20

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1840))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1840)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(920))\)\(^{\oplus 2}\)