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Properties

Label 1369.2
Level 1369
Weight 2
Dimension 76964
Nonzero newspaces 12
Sturm bound 312132
Trace bound 2

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Defining parameters

Level: \( N \) = \( 1369 = 37^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(312132\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1369))\).

Total New Old
Modular forms 79023 78873 150
Cusp forms 77044 76964 80
Eisenstein series 1979 1909 70

Trace form

\( 76964 q - 633 q^{2} - 634 q^{3} - 637 q^{4} - 636 q^{5} - 642 q^{6} - 638 q^{7} - 645 q^{8} - 643 q^{9} + O(q^{10}) \) \( 76964 q - 633 q^{2} - 634 q^{3} - 637 q^{4} - 636 q^{5} - 642 q^{6} - 638 q^{7} - 645 q^{8} - 643 q^{9} - 648 q^{10} - 642 q^{11} - 658 q^{12} - 644 q^{13} - 654 q^{14} - 654 q^{15} - 661 q^{16} - 648 q^{17} - 669 q^{18} - 650 q^{19} - 672 q^{20} - 662 q^{21} - 666 q^{22} - 654 q^{23} - 690 q^{24} - 661 q^{25} - 654 q^{26} - 622 q^{27} - 566 q^{28} - 624 q^{29} - 558 q^{30} - 554 q^{31} - 549 q^{32} - 606 q^{33} - 540 q^{34} - 570 q^{35} - 415 q^{36} - 606 q^{37} - 1230 q^{38} - 602 q^{39} - 450 q^{40} - 564 q^{41} - 582 q^{42} - 602 q^{43} - 570 q^{44} - 600 q^{45} - 558 q^{46} - 642 q^{47} - 634 q^{48} - 639 q^{49} - 705 q^{50} - 702 q^{51} - 728 q^{52} - 684 q^{53} - 750 q^{54} - 702 q^{55} - 750 q^{56} - 710 q^{57} - 684 q^{58} - 618 q^{59} - 546 q^{60} - 602 q^{61} - 546 q^{62} - 518 q^{63} - 505 q^{64} - 552 q^{65} - 270 q^{66} - 626 q^{67} - 540 q^{68} - 438 q^{69} - 378 q^{70} - 558 q^{71} - 249 q^{72} - 524 q^{73} - 504 q^{74} - 1006 q^{75} - 410 q^{76} - 582 q^{77} - 294 q^{78} - 566 q^{79} - 420 q^{80} - 463 q^{81} - 540 q^{82} - 642 q^{83} - 350 q^{84} - 576 q^{85} - 510 q^{86} - 534 q^{87} - 630 q^{88} - 630 q^{89} - 612 q^{90} - 658 q^{91} - 618 q^{92} - 650 q^{93} - 630 q^{94} - 606 q^{95} - 522 q^{96} - 584 q^{97} - 513 q^{98} - 606 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1369))\)

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
1369.2.a \(\chi_{1369}(1, \cdot)\) 1369.2.a.a 1 1
1369.2.a.b 1
1369.2.a.c 1
1369.2.a.d 1
1369.2.a.e 1
1369.2.a.f 1
1369.2.a.g 2
1369.2.a.h 2
1369.2.a.i 3
1369.2.a.j 3
1369.2.a.k 3
1369.2.a.l 3
1369.2.a.m 18
1369.2.a.n 27
1369.2.a.o 27
1369.2.b \(\chi_{1369}(1368, \cdot)\) 1369.2.b.a 2 1
1369.2.b.b 2
1369.2.b.c 2
1369.2.b.d 4
1369.2.b.e 6
1369.2.b.f 6
1369.2.b.g 18
1369.2.b.h 54
1369.2.c \(\chi_{1369}(581, \cdot)\) n/a 190 2
1369.2.e \(\chi_{1369}(582, \cdot)\) n/a 188 2
1369.2.f \(\chi_{1369}(678, \cdot)\) n/a 564 6
1369.2.h \(\chi_{1369}(300, \cdot)\) n/a 558 6
1369.2.j \(\chi_{1369}(38, \cdot)\) n/a 4140 36
1369.2.k \(\chi_{1369}(36, \cdot)\) n/a 4176 36
1369.2.l \(\chi_{1369}(10, \cdot)\) n/a 8280 72
1369.2.n \(\chi_{1369}(11, \cdot)\) n/a 8352 72
1369.2.o \(\chi_{1369}(7, \cdot)\) n/a 25056 216
1369.2.q \(\chi_{1369}(3, \cdot)\) n/a 25272 216

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1369))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1369)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 2}\)