↑

Properties

Label 2679.2
Level 2679
Weight 2
Dimension 195911
Nonzero newspaces 24
Sturm bound 1059840
Trace bound 4

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2679 = 3 \cdot 19 \cdot 47 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(1059840\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2679))\).

Total New Old
Modular forms 268272 198967 69305
Cusp forms 261649 195911 65738
Eisenstein series 6623 3056 3567

Trace form

\( 195911 q + 9 q^{2} - 347 q^{3} - 679 q^{4} + 18 q^{5} - 341 q^{6} - 676 q^{7} + 45 q^{8} - 347 q^{9} + O(q^{10}) \) \( 195911 q + 9 q^{2} - 347 q^{3} - 679 q^{4} + 18 q^{5} - 341 q^{6} - 676 q^{7} + 45 q^{8} - 347 q^{9} - 646 q^{10} + 36 q^{11} - 353 q^{12} - 706 q^{13} - 368 q^{15} - 751 q^{16} + 18 q^{17} - 359 q^{18} - 791 q^{19} - 18 q^{20} - 368 q^{21} - 700 q^{22} + 36 q^{23} - 377 q^{24} - 679 q^{25} + 54 q^{26} - 371 q^{27} - 688 q^{28} + 18 q^{29} - 422 q^{30} - 676 q^{31} + 9 q^{32} - 422 q^{33} - 718 q^{34} - 92 q^{35} - 657 q^{36} - 786 q^{37} - 227 q^{38} - 950 q^{39} - 1306 q^{40} - 222 q^{41} - 734 q^{42} - 804 q^{43} - 296 q^{44} - 616 q^{45} - 1124 q^{46} - 125 q^{47} - 1085 q^{48} - 785 q^{49} - 197 q^{50} - 454 q^{51} - 774 q^{52} + 70 q^{53} - 509 q^{54} - 760 q^{55} - 192 q^{56} - 313 q^{57} - 1406 q^{58} + 88 q^{59} - 282 q^{60} - 726 q^{61} + 108 q^{62} - 278 q^{63} - 607 q^{64} + 36 q^{65} - 242 q^{66} - 784 q^{67} + 126 q^{68} - 368 q^{69} - 700 q^{70} + 72 q^{71} - 431 q^{72} - 802 q^{73} + 54 q^{74} - 443 q^{75} - 925 q^{76} - 292 q^{77} - 788 q^{78} - 1236 q^{79} - 590 q^{80} - 419 q^{81} - 1834 q^{82} - 184 q^{83} - 1166 q^{84} - 1544 q^{85} - 736 q^{86} - 732 q^{87} - 1912 q^{88} - 422 q^{89} - 606 q^{90} - 1620 q^{91} - 792 q^{92} - 688 q^{93} - 1735 q^{94} - 242 q^{95} - 1345 q^{96} - 882 q^{97} - 603 q^{98} - 516 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2679))\)

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
2679.2.a \(\chi_{2679}(1, \cdot)\) 2679.2.a.a 1 1
2679.2.a.b 1
2679.2.a.c 1
2679.2.a.d 1
2679.2.a.e 3
2679.2.a.f 3
2679.2.a.g 4
2679.2.a.h 4
2679.2.a.i 6
2679.2.a.j 7
2679.2.a.k 7
2679.2.a.l 7
2679.2.a.m 23
2679.2.a.n 23
2679.2.a.o 24
2679.2.a.p 24
2679.2.c \(\chi_{2679}(892, \cdot)\) n/a 160 1
2679.2.d \(\chi_{2679}(704, \cdot)\) n/a 288 1
2679.2.f \(\chi_{2679}(1082, \cdot)\) n/a 308 1
2679.2.i \(\chi_{2679}(847, \cdot)\) n/a 304 2
2679.2.l \(\chi_{2679}(236, \cdot)\) n/a 616 2
2679.2.n \(\chi_{2679}(140, \cdot)\) n/a 632 2
2679.2.o \(\chi_{2679}(46, \cdot)\) n/a 320 2
2679.2.q \(\chi_{2679}(142, \cdot)\) n/a 924 6
2679.2.s \(\chi_{2679}(659, \cdot)\) n/a 1836 6
2679.2.v \(\chi_{2679}(422, \cdot)\) n/a 1896 6
2679.2.w \(\chi_{2679}(469, \cdot)\) n/a 960 6
2679.2.y \(\chi_{2679}(115, \cdot)\) n/a 3168 22
2679.2.bb \(\chi_{2679}(56, \cdot)\) n/a 6952 22
2679.2.bd \(\chi_{2679}(20, \cdot)\) n/a 6336 22
2679.2.be \(\chi_{2679}(151, \cdot)\) n/a 3520 22
2679.2.bg \(\chi_{2679}(7, \cdot)\) n/a 7040 44
2679.2.bi \(\chi_{2679}(31, \cdot)\) n/a 7040 44
2679.2.bj \(\chi_{2679}(11, \cdot)\) n/a 13904 44
2679.2.bl \(\chi_{2679}(8, \cdot)\) n/a 13904 44
2679.2.bo \(\chi_{2679}(4, \cdot)\) n/a 21120 132
2679.2.bq \(\chi_{2679}(10, \cdot)\) n/a 21120 132
2679.2.br \(\chi_{2679}(5, \cdot)\) n/a 41712 132
2679.2.bu \(\chi_{2679}(2, \cdot)\) n/a 41712 132

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2679))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2679)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(141))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(893))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2679))\)\(^{\oplus 1}\)