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Properties

Label 1681.2
Level 1681
Weight 2
Dimension 116349
Nonzero newspaces 12
Sturm bound 470680
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1681 = 41^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(470680\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1681))\).

Total New Old
Modular forms 118890 118710 180
Cusp forms 116451 116349 102
Eisenstein series 2439 2361 78

Trace form

\( 116349 q - 783 q^{2} - 784 q^{3} - 787 q^{4} - 786 q^{5} - 792 q^{6} - 788 q^{7} - 795 q^{8} - 793 q^{9} + O(q^{10}) \) \( 116349 q - 783 q^{2} - 784 q^{3} - 787 q^{4} - 786 q^{5} - 792 q^{6} - 788 q^{7} - 795 q^{8} - 793 q^{9} - 798 q^{10} - 792 q^{11} - 808 q^{12} - 794 q^{13} - 804 q^{14} - 804 q^{15} - 811 q^{16} - 798 q^{17} - 819 q^{18} - 800 q^{19} - 822 q^{20} - 812 q^{21} - 816 q^{22} - 804 q^{23} - 840 q^{24} - 811 q^{25} - 822 q^{26} - 820 q^{27} - 836 q^{28} - 810 q^{29} - 772 q^{30} - 772 q^{31} - 703 q^{32} - 708 q^{33} - 734 q^{34} - 748 q^{35} - 591 q^{36} - 698 q^{37} - 760 q^{38} - 676 q^{39} - 590 q^{40} - 780 q^{41} - 1316 q^{42} - 784 q^{43} - 624 q^{44} - 698 q^{45} - 772 q^{46} - 708 q^{47} - 624 q^{48} - 757 q^{49} - 773 q^{50} - 732 q^{51} - 738 q^{52} - 794 q^{53} - 820 q^{54} - 852 q^{55} - 900 q^{56} - 860 q^{57} - 870 q^{58} - 840 q^{59} - 948 q^{60} - 842 q^{61} - 876 q^{62} - 884 q^{63} - 907 q^{64} - 844 q^{65} - 764 q^{66} - 728 q^{67} - 706 q^{68} - 716 q^{69} - 524 q^{70} - 692 q^{71} - 615 q^{72} - 694 q^{73} - 654 q^{74} - 584 q^{75} - 320 q^{76} - 716 q^{77} - 548 q^{78} - 700 q^{79} - 486 q^{80} - 521 q^{81} - 560 q^{82} - 1464 q^{83} - 444 q^{84} - 548 q^{85} - 512 q^{86} - 740 q^{87} - 560 q^{88} - 710 q^{89} - 414 q^{90} - 572 q^{91} - 708 q^{92} - 748 q^{93} - 564 q^{94} - 740 q^{95} - 632 q^{96} - 718 q^{97} - 751 q^{98} - 816 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1681))\)

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
1681.2.a \(\chi_{1681}(1, \cdot)\) 1681.2.a.a 2 1
1681.2.a.b 3
1681.2.a.c 3
1681.2.a.d 3
1681.2.a.e 4
1681.2.a.f 4
1681.2.a.g 6
1681.2.a.h 8
1681.2.a.i 12
1681.2.a.j 12
1681.2.a.k 18
1681.2.a.l 18
1681.2.a.m 24
1681.2.b \(\chi_{1681}(1680, \cdot)\) n/a 118 1
1681.2.c \(\chi_{1681}(378, \cdot)\) n/a 234 2
1681.2.d \(\chi_{1681}(51, \cdot)\) n/a 472 4
1681.2.f \(\chi_{1681}(148, \cdot)\) n/a 472 4
1681.2.g \(\chi_{1681}(207, \cdot)\) n/a 936 8
1681.2.i \(\chi_{1681}(42, \cdot)\) n/a 5680 40
1681.2.j \(\chi_{1681}(40, \cdot)\) n/a 5680 40
1681.2.k \(\chi_{1681}(9, \cdot)\) n/a 11440 80
1681.2.l \(\chi_{1681}(10, \cdot)\) n/a 22720 160
1681.2.n \(\chi_{1681}(4, \cdot)\) n/a 22720 160
1681.2.o \(\chi_{1681}(2, \cdot)\) n/a 45760 320

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1681))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1681)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1681))\)\(^{\oplus 1}\)