Properties

Label 2023.2
Level 2023
Weight 2
Dimension 156585
Nonzero newspaces 20
Sturm bound 665856
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(665856\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2023))\).

Total New Old
Modular forms 168864 160269 8595
Cusp forms 164065 156585 7480
Eisenstein series 4799 3684 1115

Trace form

\( 156585 q - 477 q^{2} - 476 q^{3} - 473 q^{4} - 474 q^{5} - 468 q^{6} - 599 q^{7} - 1185 q^{8} - 467 q^{9} + O(q^{10}) \) \( 156585 q - 477 q^{2} - 476 q^{3} - 473 q^{4} - 474 q^{5} - 468 q^{6} - 599 q^{7} - 1185 q^{8} - 467 q^{9} - 478 q^{10} - 500 q^{11} - 548 q^{12} - 498 q^{13} - 629 q^{14} - 1272 q^{15} - 593 q^{16} - 528 q^{17} - 1017 q^{18} - 492 q^{19} - 550 q^{20} - 644 q^{21} - 1228 q^{22} - 488 q^{23} - 580 q^{24} - 561 q^{25} - 582 q^{26} - 536 q^{27} - 689 q^{28} - 1250 q^{29} - 664 q^{30} - 576 q^{31} - 641 q^{32} - 592 q^{33} - 640 q^{34} - 1218 q^{35} - 1429 q^{36} - 570 q^{37} - 612 q^{38} - 616 q^{39} - 774 q^{40} - 614 q^{41} - 780 q^{42} - 1316 q^{43} - 780 q^{44} - 610 q^{45} - 600 q^{46} - 592 q^{47} - 772 q^{48} - 663 q^{49} - 1363 q^{50} - 576 q^{51} - 1086 q^{52} - 602 q^{53} - 840 q^{54} - 664 q^{55} - 825 q^{56} - 1504 q^{57} - 742 q^{58} - 676 q^{59} - 984 q^{60} - 674 q^{61} - 800 q^{62} - 827 q^{63} - 1521 q^{64} - 700 q^{65} - 848 q^{66} - 572 q^{67} - 712 q^{68} - 1280 q^{69} - 854 q^{70} - 1320 q^{71} - 1069 q^{72} - 806 q^{73} - 702 q^{74} - 868 q^{75} - 820 q^{76} - 748 q^{77} - 1704 q^{78} - 656 q^{79} - 998 q^{80} - 775 q^{81} - 786 q^{82} - 652 q^{83} - 940 q^{84} - 1464 q^{85} - 1244 q^{86} - 744 q^{87} - 940 q^{88} - 678 q^{89} - 1158 q^{90} - 810 q^{91} - 1800 q^{92} - 736 q^{93} - 976 q^{94} - 808 q^{95} - 708 q^{96} - 638 q^{97} - 885 q^{98} - 1460 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2023))\)

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
2023.2.a \(\chi_{2023}(1, \cdot)\) 2023.2.a.a 1 1
2023.2.a.b 1
2023.2.a.c 3
2023.2.a.d 3
2023.2.a.e 4
2023.2.a.f 4
2023.2.a.g 4
2023.2.a.h 5
2023.2.a.i 5
2023.2.a.j 5
2023.2.a.k 9
2023.2.a.l 9
2023.2.a.m 10
2023.2.a.n 10
2023.2.a.o 15
2023.2.a.p 15
2023.2.a.q 16
2023.2.a.r 16
2023.2.b \(\chi_{2023}(288, \cdot)\) n/a 134 1
2023.2.e \(\chi_{2023}(1157, \cdot)\) n/a 332 2
2023.2.g \(\chi_{2023}(540, \cdot)\) n/a 268 2
2023.2.j \(\chi_{2023}(1444, \cdot)\) n/a 332 2
2023.2.k \(\chi_{2023}(134, \cdot)\) n/a 544 4
2023.2.n \(\chi_{2023}(905, \cdot)\) n/a 664 4
2023.2.p \(\chi_{2023}(447, \cdot)\) n/a 1328 8
2023.2.q \(\chi_{2023}(120, \cdot)\) n/a 2464 16
2023.2.r \(\chi_{2023}(179, \cdot)\) n/a 1328 8
2023.2.v \(\chi_{2023}(50, \cdot)\) n/a 2464 16
2023.2.w \(\chi_{2023}(40, \cdot)\) n/a 2656 16
2023.2.y \(\chi_{2023}(18, \cdot)\) n/a 6464 32
2023.2.z \(\chi_{2023}(64, \cdot)\) n/a 4928 32
2023.2.bb \(\chi_{2023}(16, \cdot)\) n/a 6464 32
2023.2.bf \(\chi_{2023}(8, \cdot)\) n/a 9728 64
2023.2.bg \(\chi_{2023}(4, \cdot)\) n/a 12928 64
2023.2.bi \(\chi_{2023}(6, \cdot)\) n/a 25856 128
2023.2.bl \(\chi_{2023}(2, \cdot)\) n/a 25856 128
2023.2.bn \(\chi_{2023}(3, \cdot)\) n/a 51712 256

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2023))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2023)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 2}\)