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Properties

Label 2645.2
Level 2645
Weight 2
Dimension 252957
Nonzero newspaces 12
Sturm bound 1117248
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2645 = 5 \cdot 23^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(1117248\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2645))\).

Total New Old
Modular forms 282304 257183 25121
Cusp forms 276321 252957 23364
Eisenstein series 5983 4226 1757

Trace form

\( 252957 q - 459 q^{2} - 458 q^{3} - 455 q^{4} - 692 q^{5} - 1374 q^{6} - 454 q^{7} - 447 q^{8} - 449 q^{9} + O(q^{10}) \) \( 252957 q - 459 q^{2} - 458 q^{3} - 455 q^{4} - 692 q^{5} - 1374 q^{6} - 454 q^{7} - 447 q^{8} - 449 q^{9} - 690 q^{10} - 1374 q^{11} - 434 q^{12} - 448 q^{13} - 438 q^{14} - 711 q^{15} - 1443 q^{16} - 488 q^{17} - 599 q^{18} - 486 q^{19} - 774 q^{20} - 1486 q^{21} - 558 q^{22} - 528 q^{23} - 1106 q^{24} - 736 q^{25} - 1432 q^{26} - 554 q^{27} - 582 q^{28} - 476 q^{29} - 769 q^{30} - 1398 q^{31} - 487 q^{32} - 458 q^{33} - 496 q^{34} - 729 q^{35} - 1515 q^{36} - 600 q^{37} - 622 q^{38} - 582 q^{39} - 854 q^{40} - 1432 q^{41} - 806 q^{42} - 594 q^{43} - 774 q^{44} - 834 q^{45} - 1628 q^{46} - 1030 q^{47} - 778 q^{48} - 669 q^{49} - 734 q^{50} - 1490 q^{51} - 804 q^{52} - 496 q^{53} - 782 q^{54} - 813 q^{55} - 1750 q^{56} - 690 q^{57} - 768 q^{58} - 666 q^{59} - 929 q^{60} - 1500 q^{61} - 630 q^{62} - 578 q^{63} - 687 q^{64} - 833 q^{65} - 1726 q^{66} - 482 q^{67} - 908 q^{68} - 594 q^{69} - 1505 q^{70} - 1534 q^{71} - 927 q^{72} - 476 q^{73} - 744 q^{74} - 931 q^{75} - 1818 q^{76} - 762 q^{77} - 998 q^{78} - 734 q^{79} - 1080 q^{80} - 1969 q^{81} - 776 q^{82} - 686 q^{83} - 1118 q^{84} - 939 q^{85} - 1782 q^{86} - 870 q^{87} - 458 q^{88} - 636 q^{89} - 1116 q^{90} - 1670 q^{91} - 682 q^{92} - 1302 q^{93} - 802 q^{94} - 783 q^{95} - 1970 q^{96} - 496 q^{97} - 467 q^{98} - 614 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2645))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2645.2.a \(\chi_{2645}(1, \cdot)\) 2645.2.a.a 1 1
2645.2.a.b 1
2645.2.a.c 1
2645.2.a.d 2
2645.2.a.e 2
2645.2.a.f 2
2645.2.a.g 2
2645.2.a.h 2
2645.2.a.i 4
2645.2.a.j 4
2645.2.a.k 4
2645.2.a.l 4
2645.2.a.m 4
2645.2.a.n 5
2645.2.a.o 5
2645.2.a.p 6
2645.2.a.q 6
2645.2.a.r 6
2645.2.a.s 6
2645.2.a.t 10
2645.2.a.u 10
2645.2.a.v 16
2645.2.a.w 16
2645.2.a.x 25
2645.2.a.y 25
2645.2.b \(\chi_{2645}(1059, \cdot)\) n/a 232 1
2645.2.e \(\chi_{2645}(528, \cdot)\) n/a 464 2
2645.2.g \(\chi_{2645}(266, \cdot)\) n/a 1680 10
2645.2.j \(\chi_{2645}(334, \cdot)\) n/a 2320 10
2645.2.k \(\chi_{2645}(116, \cdot)\) n/a 4048 22
2645.2.m \(\chi_{2645}(28, \cdot)\) n/a 4640 20
2645.2.p \(\chi_{2645}(24, \cdot)\) n/a 6028 22
2645.2.r \(\chi_{2645}(22, \cdot)\) n/a 12056 44
2645.2.s \(\chi_{2645}(6, \cdot)\) n/a 40480 220
2645.2.t \(\chi_{2645}(4, \cdot)\) n/a 60280 220
2645.2.w \(\chi_{2645}(7, \cdot)\) n/a 120560 440

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2645))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2645)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 2}\)