↑

Properties

Label 2682.2
Level 2682
Weight 2
Dimension 52721
Nonzero newspaces 12
Sturm bound 799200
Trace bound 4

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2682 = 2 \cdot 3^{2} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(799200\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2682))\).

Total New Old
Modular forms 202168 52721 149447
Cusp forms 197433 52721 144712
Eisenstein series 4735 0 4735

Trace form

\( 52721 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} + O(q^{10}) \) \( 52721 q + 2 q^{2} + 6 q^{3} + 2 q^{4} - 6 q^{6} + 4 q^{7} - 4 q^{8} - 6 q^{9} - 6 q^{11} + 4 q^{13} + 4 q^{14} + 2 q^{16} + 12 q^{17} + 12 q^{18} + 4 q^{19} - 12 q^{21} - 6 q^{22} - 12 q^{23} + 6 q^{24} - 10 q^{25} - 8 q^{26} - 8 q^{28} + 12 q^{29} - 8 q^{31} + 2 q^{32} + 18 q^{33} - 6 q^{34} - 6 q^{36} + 16 q^{37} - 2 q^{38} + 18 q^{41} - 2 q^{43} + 12 q^{44} + 24 q^{46} - 12 q^{47} - 6 q^{48} - 6 q^{49} - 10 q^{50} - 18 q^{51} + 4 q^{52} - 48 q^{53} - 18 q^{54} + 4 q^{56} - 6 q^{57} + 12 q^{58} + 6 q^{59} + 16 q^{61} + 16 q^{62} + 24 q^{63} - 4 q^{64} + 10 q^{67} - 6 q^{68} + 48 q^{71} - 6 q^{72} - 44 q^{73} - 8 q^{74} + 30 q^{75} - 2 q^{76} - 12 q^{77} + 12 q^{78} - 8 q^{79} + 18 q^{81} - 36 q^{82} + 24 q^{83} + 12 q^{84} - 2 q^{86} - 36 q^{87} - 6 q^{88} - 24 q^{89} - 16 q^{91} - 12 q^{92} - 12 q^{94} + 10 q^{97} + 12 q^{98} - 36 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2682))\)

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
2682.2.a \(\chi_{2682}(1, \cdot)\) 2682.2.a.a 1 1
2682.2.a.b 1
2682.2.a.c 1
2682.2.a.d 1
2682.2.a.e 1
2682.2.a.f 1
2682.2.a.g 1
2682.2.a.h 1
2682.2.a.i 1
2682.2.a.j 1
2682.2.a.k 1
2682.2.a.l 1
2682.2.a.m 1
2682.2.a.n 1
2682.2.a.o 1
2682.2.a.p 1
2682.2.a.q 1
2682.2.a.r 2
2682.2.a.s 2
2682.2.a.t 3
2682.2.a.u 3
2682.2.a.v 4
2682.2.a.w 4
2682.2.a.x 4
2682.2.a.y 4
2682.2.a.z 5
2682.2.a.ba 5
2682.2.a.bb 5
2682.2.a.bc 5
2682.2.d \(\chi_{2682}(595, \cdot)\) 2682.2.d.a 2 1
2682.2.d.b 2
2682.2.d.c 2
2682.2.d.d 2
2682.2.d.e 4
2682.2.d.f 10
2682.2.d.g 12
2682.2.d.h 12
2682.2.d.i 16
2682.2.e \(\chi_{2682}(895, \cdot)\) n/a 296 2
2682.2.f \(\chi_{2682}(701, \cdot)\) 2682.2.f.a 16 2
2682.2.f.b 32
2682.2.f.c 52
2682.2.h \(\chi_{2682}(1489, \cdot)\) n/a 300 2
2682.2.l \(\chi_{2682}(491, \cdot)\) n/a 600 4
2682.2.m \(\chi_{2682}(19, \cdot)\) n/a 2268 36
2682.2.n \(\chi_{2682}(217, \cdot)\) n/a 2232 36
2682.2.q \(\chi_{2682}(25, \cdot)\) n/a 10800 72
2682.2.s \(\chi_{2682}(71, \cdot)\) n/a 3600 72
2682.2.v \(\chi_{2682}(7, \cdot)\) n/a 10800 72
2682.2.w \(\chi_{2682}(11, \cdot)\) n/a 21600 144

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2682))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2682)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(149))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(298))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(447))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(894))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1341))\)\(^{\oplus 2}\)