Properties

Label 1859.2
Level 1859
Weight 2
Dimension 136108
Nonzero newspaces 24
Sturm bound 567840
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(567840\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1859))\).

Total New Old
Modular forms 144240 139788 4452
Cusp forms 139681 136108 3573
Eisenstein series 4559 3680 879

Trace form

\( 136108 q - 527 q^{2} - 525 q^{3} - 519 q^{4} - 521 q^{5} - 514 q^{6} - 530 q^{7} - 549 q^{8} - 549 q^{9} + O(q^{10}) \) \( 136108 q - 527 q^{2} - 525 q^{3} - 519 q^{4} - 521 q^{5} - 514 q^{6} - 530 q^{7} - 549 q^{8} - 549 q^{9} - 572 q^{10} - 604 q^{11} - 1266 q^{12} - 600 q^{13} - 1028 q^{14} - 553 q^{15} - 581 q^{16} - 548 q^{17} - 617 q^{18} - 588 q^{19} - 616 q^{20} - 598 q^{21} - 653 q^{22} - 1213 q^{23} - 708 q^{24} - 585 q^{25} - 636 q^{26} - 1107 q^{27} - 676 q^{28} - 606 q^{29} - 742 q^{30} - 593 q^{31} - 721 q^{32} - 675 q^{33} - 1322 q^{34} - 650 q^{35} - 777 q^{36} - 555 q^{37} - 636 q^{38} - 640 q^{39} - 1206 q^{40} - 674 q^{41} - 796 q^{42} - 674 q^{43} - 741 q^{44} - 1412 q^{45} - 790 q^{46} - 640 q^{47} - 832 q^{48} - 706 q^{49} - 799 q^{50} - 766 q^{51} - 742 q^{52} - 1152 q^{53} - 826 q^{54} - 719 q^{55} - 1524 q^{56} - 744 q^{57} - 738 q^{58} - 631 q^{59} - 1010 q^{60} - 682 q^{61} - 782 q^{62} - 812 q^{63} - 901 q^{64} - 738 q^{65} - 1384 q^{66} - 1351 q^{67} - 898 q^{68} - 743 q^{69} - 932 q^{70} - 699 q^{71} - 1077 q^{72} - 722 q^{73} - 912 q^{74} - 888 q^{75} - 948 q^{76} - 768 q^{77} - 1644 q^{78} - 1178 q^{79} - 1126 q^{80} - 822 q^{81} - 830 q^{82} - 762 q^{83} - 1172 q^{84} - 794 q^{85} - 888 q^{86} - 888 q^{87} - 927 q^{88} - 1467 q^{89} - 1178 q^{90} - 772 q^{91} - 1418 q^{92} - 943 q^{93} - 976 q^{94} - 840 q^{95} - 1268 q^{96} - 757 q^{97} - 927 q^{98} - 883 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1859))\)

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
1859.2.a \(\chi_{1859}(1, \cdot)\) 1859.2.a.a 1 1
1859.2.a.b 1
1859.2.a.c 2
1859.2.a.d 2
1859.2.a.e 3
1859.2.a.f 3
1859.2.a.g 3
1859.2.a.h 3
1859.2.a.i 4
1859.2.a.j 6
1859.2.a.k 6
1859.2.a.l 6
1859.2.a.m 6
1859.2.a.n 6
1859.2.a.o 8
1859.2.a.p 8
1859.2.a.q 9
1859.2.a.r 9
1859.2.a.s 21
1859.2.a.t 21
1859.2.b \(\chi_{1859}(1013, \cdot)\) n/a 128 1
1859.2.e \(\chi_{1859}(529, \cdot)\) n/a 256 2
1859.2.g \(\chi_{1859}(1253, \cdot)\) n/a 288 2
1859.2.h \(\chi_{1859}(170, \cdot)\) n/a 576 4
1859.2.j \(\chi_{1859}(23, \cdot)\) n/a 260 2
1859.2.n \(\chi_{1859}(168, \cdot)\) n/a 576 4
1859.2.o \(\chi_{1859}(934, \cdot)\) n/a 576 4
1859.2.q \(\chi_{1859}(144, \cdot)\) n/a 1848 12
1859.2.r \(\chi_{1859}(146, \cdot)\) n/a 1152 8
1859.2.t \(\chi_{1859}(239, \cdot)\) n/a 1152 8
1859.2.w \(\chi_{1859}(12, \cdot)\) n/a 1824 12
1859.2.y \(\chi_{1859}(147, \cdot)\) n/a 1152 8
1859.2.ba \(\chi_{1859}(100, \cdot)\) n/a 3648 24
1859.2.bb \(\chi_{1859}(21, \cdot)\) n/a 4320 24
1859.2.bd \(\chi_{1859}(19, \cdot)\) n/a 2304 16
1859.2.bf \(\chi_{1859}(14, \cdot)\) n/a 8640 48
1859.2.bh \(\chi_{1859}(56, \cdot)\) n/a 3600 24
1859.2.bj \(\chi_{1859}(25, \cdot)\) n/a 8640 48
1859.2.bn \(\chi_{1859}(32, \cdot)\) n/a 8640 48
1859.2.bo \(\chi_{1859}(3, \cdot)\) n/a 17280 96
1859.2.bp \(\chi_{1859}(8, \cdot)\) n/a 17280 96
1859.2.bs \(\chi_{1859}(4, \cdot)\) n/a 17280 96
1859.2.bv \(\chi_{1859}(2, \cdot)\) n/a 34560 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1859))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1859)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)