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Properties

Label 1511.2
Level 1511
Weight 2
Dimension 94376
Nonzero newspaces 4
Sturm bound 380520
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1511 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(380520\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1511))\).

Total New Old
Modular forms 95885 95885 0
Cusp forms 94376 94376 0
Eisenstein series 1509 1509 0

Trace form

\( 94376 q - 752 q^{2} - 751 q^{3} - 748 q^{4} - 749 q^{5} - 743 q^{6} - 747 q^{7} - 740 q^{8} - 742 q^{9} + O(q^{10}) \) \( 94376 q - 752 q^{2} - 751 q^{3} - 748 q^{4} - 749 q^{5} - 743 q^{6} - 747 q^{7} - 740 q^{8} - 742 q^{9} - 737 q^{10} - 743 q^{11} - 727 q^{12} - 741 q^{13} - 731 q^{14} - 731 q^{15} - 724 q^{16} - 737 q^{17} - 716 q^{18} - 735 q^{19} - 713 q^{20} - 723 q^{21} - 719 q^{22} - 731 q^{23} - 695 q^{24} - 724 q^{25} - 713 q^{26} - 715 q^{27} - 699 q^{28} - 725 q^{29} - 683 q^{30} - 723 q^{31} - 692 q^{32} - 707 q^{33} - 701 q^{34} - 707 q^{35} - 664 q^{36} - 717 q^{37} - 695 q^{38} - 699 q^{39} - 665 q^{40} - 713 q^{41} - 659 q^{42} - 711 q^{43} - 671 q^{44} - 677 q^{45} - 683 q^{46} - 707 q^{47} - 631 q^{48} - 698 q^{49} - 662 q^{50} - 683 q^{51} - 657 q^{52} - 701 q^{53} - 635 q^{54} - 683 q^{55} - 635 q^{56} - 675 q^{57} - 665 q^{58} - 695 q^{59} - 587 q^{60} - 693 q^{61} - 659 q^{62} - 651 q^{63} - 628 q^{64} - 671 q^{65} - 611 q^{66} - 687 q^{67} - 629 q^{68} - 659 q^{69} - 611 q^{70} - 683 q^{71} - 560 q^{72} - 681 q^{73} - 641 q^{74} - 631 q^{75} - 615 q^{76} - 659 q^{77} - 587 q^{78} - 675 q^{79} - 569 q^{80} - 634 q^{81} - 629 q^{82} - 671 q^{83} - 531 q^{84} - 647 q^{85} - 623 q^{86} - 635 q^{87} - 575 q^{88} - 665 q^{89} - 521 q^{90} - 643 q^{91} - 587 q^{92} - 627 q^{93} - 611 q^{94} - 635 q^{95} - 503 q^{96} - 657 q^{97} - 584 q^{98} - 599 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1511))\)

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
1511.2.a \(\chi_{1511}(1, \cdot)\) 1511.2.a.a 39 1
1511.2.a.b 87
1511.2.c \(\chi_{1511}(534, \cdot)\) n/a 500 4
1511.2.e \(\chi_{1511}(3, \cdot)\) n/a 18750 150
1511.2.g \(\chi_{1511}(2, \cdot)\) n/a 75000 600

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