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Properties

Label 1601.2
Level 1601
Weight 2
Dimension 106001
Nonzero newspaces 18
Sturm bound 427200
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1601 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(427200\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1601))\).

Total New Old
Modular forms 107600 107600 0
Cusp forms 106001 106001 0
Eisenstein series 1599 1599 0

Trace form

\( 106001 q - 797 q^{2} - 796 q^{3} - 793 q^{4} - 794 q^{5} - 788 q^{6} - 792 q^{7} - 785 q^{8} - 787 q^{9} + O(q^{10}) \) \( 106001 q - 797 q^{2} - 796 q^{3} - 793 q^{4} - 794 q^{5} - 788 q^{6} - 792 q^{7} - 785 q^{8} - 787 q^{9} - 782 q^{10} - 788 q^{11} - 772 q^{12} - 786 q^{13} - 776 q^{14} - 776 q^{15} - 769 q^{16} - 782 q^{17} - 761 q^{18} - 780 q^{19} - 758 q^{20} - 768 q^{21} - 764 q^{22} - 776 q^{23} - 740 q^{24} - 769 q^{25} - 758 q^{26} - 760 q^{27} - 744 q^{28} - 770 q^{29} - 728 q^{30} - 768 q^{31} - 737 q^{32} - 752 q^{33} - 746 q^{34} - 752 q^{35} - 709 q^{36} - 762 q^{37} - 740 q^{38} - 744 q^{39} - 710 q^{40} - 758 q^{41} - 704 q^{42} - 756 q^{43} - 716 q^{44} - 722 q^{45} - 728 q^{46} - 752 q^{47} - 676 q^{48} - 743 q^{49} - 707 q^{50} - 728 q^{51} - 702 q^{52} - 746 q^{53} - 680 q^{54} - 728 q^{55} - 680 q^{56} - 720 q^{57} - 710 q^{58} - 740 q^{59} - 632 q^{60} - 738 q^{61} - 704 q^{62} - 696 q^{63} - 673 q^{64} - 716 q^{65} - 656 q^{66} - 732 q^{67} - 674 q^{68} - 704 q^{69} - 656 q^{70} - 728 q^{71} - 605 q^{72} - 726 q^{73} - 686 q^{74} - 676 q^{75} - 660 q^{76} - 704 q^{77} - 632 q^{78} - 720 q^{79} - 614 q^{80} - 679 q^{81} - 674 q^{82} - 716 q^{83} - 576 q^{84} - 692 q^{85} - 668 q^{86} - 680 q^{87} - 620 q^{88} - 710 q^{89} - 566 q^{90} - 688 q^{91} - 632 q^{92} - 672 q^{93} - 656 q^{94} - 680 q^{95} - 548 q^{96} - 702 q^{97} - 629 q^{98} - 644 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1601))\)

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
1601.2.a \(\chi_{1601}(1, \cdot)\) 1601.2.a.a 53 1
1601.2.a.b 80
1601.2.b \(\chi_{1601}(1600, \cdot)\) n/a 132 1
1601.2.c \(\chi_{1601}(40, \cdot)\) n/a 264 2
1601.2.d \(\chi_{1601}(42, \cdot)\) n/a 528 4
1601.2.e \(\chi_{1601}(310, \cdot)\) n/a 528 4
1601.2.f \(\chi_{1601}(648, \cdot)\) n/a 528 4
1601.2.g \(\chi_{1601}(257, \cdot)\) n/a 1056 8
1601.2.h \(\chi_{1601}(69, \cdot)\) n/a 1056 8
1601.2.i \(\chi_{1601}(19, \cdot)\) n/a 2640 20
1601.2.j \(\chi_{1601}(109, \cdot)\) n/a 2128 16
1601.2.k \(\chi_{1601}(212, \cdot)\) n/a 2112 16
1601.2.l \(\chi_{1601}(61, \cdot)\) n/a 2640 20
1601.2.n \(\chi_{1601}(32, \cdot)\) n/a 4224 32
1601.2.o \(\chi_{1601}(16, \cdot)\) n/a 5280 40
1601.2.p \(\chi_{1601}(43, \cdot)\) n/a 8512 64
1601.2.q \(\chi_{1601}(4, \cdot)\) n/a 10560 80
1601.2.s \(\chi_{1601}(2, \cdot)\) n/a 21120 160
1601.2.t \(\chi_{1601}(9, \cdot)\) n/a 42560 320

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