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Properties

Label 2768.2
Level 2768
Weight 2
Dimension 133898
Nonzero newspaces 14
Sturm bound 957696
Trace bound 3

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Defining parameters

Level: \( N \) = \( 2768 = 2^{4} \cdot 173 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(957696\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2768))\).

Total New Old
Modular forms 241832 135436 106396
Cusp forms 237017 133898 103119
Eisenstein series 4815 1538 3277

Trace form

\( 133898 q - 340 q^{2} - 254 q^{3} - 344 q^{4} - 426 q^{5} - 352 q^{6} - 258 q^{7} - 352 q^{8} - 86 q^{9} + O(q^{10}) \) \( 133898 q - 340 q^{2} - 254 q^{3} - 344 q^{4} - 426 q^{5} - 352 q^{6} - 258 q^{7} - 352 q^{8} - 86 q^{9} - 344 q^{10} - 262 q^{11} - 336 q^{12} - 426 q^{13} - 336 q^{14} - 266 q^{15} - 328 q^{16} - 766 q^{17} - 348 q^{18} - 270 q^{19} - 352 q^{20} - 438 q^{21} - 344 q^{22} - 258 q^{23} - 344 q^{24} - 86 q^{25} - 352 q^{26} - 242 q^{27} - 360 q^{28} - 442 q^{29} - 336 q^{30} - 226 q^{31} - 360 q^{32} - 766 q^{33} - 352 q^{34} - 250 q^{35} - 336 q^{36} - 442 q^{37} - 320 q^{38} - 258 q^{39} - 328 q^{40} - 86 q^{41} - 344 q^{42} - 278 q^{43} - 336 q^{44} - 434 q^{45} - 368 q^{46} - 290 q^{47} - 360 q^{48} - 786 q^{49} - 332 q^{50} - 266 q^{51} - 336 q^{52} - 410 q^{53} - 344 q^{54} - 258 q^{55} - 328 q^{56} - 86 q^{57} - 320 q^{58} - 246 q^{59} - 344 q^{60} - 394 q^{61} - 376 q^{62} - 266 q^{63} - 344 q^{64} - 782 q^{65} - 352 q^{66} - 238 q^{67} - 344 q^{68} - 406 q^{69} - 360 q^{70} - 258 q^{71} - 352 q^{72} - 86 q^{73} - 344 q^{74} - 270 q^{75} - 368 q^{76} - 438 q^{77} - 336 q^{78} - 258 q^{79} - 360 q^{80} - 794 q^{81} - 344 q^{82} - 254 q^{83} - 328 q^{84} - 438 q^{85} - 344 q^{86} - 258 q^{87} - 360 q^{88} - 86 q^{89} - 336 q^{90} - 266 q^{91} - 296 q^{92} - 462 q^{93} - 312 q^{94} - 234 q^{95} - 312 q^{96} - 766 q^{97} - 332 q^{98} - 254 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2768))\)

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
2768.2.a \(\chi_{2768}(1, \cdot)\) 2768.2.a.a 1 1
2768.2.a.b 1
2768.2.a.c 1
2768.2.a.d 1
2768.2.a.e 3
2768.2.a.f 4
2768.2.a.g 4
2768.2.a.h 4
2768.2.a.i 5
2768.2.a.j 8
2768.2.a.k 10
2768.2.a.l 10
2768.2.a.m 10
2768.2.a.n 11
2768.2.a.o 13
2768.2.b \(\chi_{2768}(1729, \cdot)\) 2768.2.b.a 2 1
2768.2.b.b 12
2768.2.b.c 14
2768.2.b.d 14
2768.2.b.e 44
2768.2.c \(\chi_{2768}(1385, \cdot)\) None 0 1
2768.2.h \(\chi_{2768}(345, \cdot)\) None 0 1
2768.2.i \(\chi_{2768}(1131, \cdot)\) n/a 692 2
2768.2.l \(\chi_{2768}(693, \cdot)\) n/a 688 2
2768.2.n \(\chi_{2768}(1823, \cdot)\) n/a 174 2
2768.2.p \(\chi_{2768}(439, \cdot)\) None 0 2
2768.2.r \(\chi_{2768}(1037, \cdot)\) n/a 692 2
2768.2.t \(\chi_{2768}(1291, \cdot)\) n/a 692 2
2768.2.u \(\chi_{2768}(81, \cdot)\) n/a 3612 42
2768.2.v \(\chi_{2768}(9, \cdot)\) None 0 42
2768.2.ba \(\chi_{2768}(57, \cdot)\) None 0 42
2768.2.bb \(\chi_{2768}(33, \cdot)\) n/a 3612 42
2768.2.bc \(\chi_{2768}(11, \cdot)\) n/a 29064 84
2768.2.be \(\chi_{2768}(13, \cdot)\) n/a 29064 84
2768.2.bg \(\chi_{2768}(7, \cdot)\) None 0 84
2768.2.bi \(\chi_{2768}(63, \cdot)\) n/a 7308 84
2768.2.bk \(\chi_{2768}(29, \cdot)\) n/a 29064 84
2768.2.bn \(\chi_{2768}(3, \cdot)\) n/a 29064 84

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2768))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2768)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(173))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(346))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(692))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1384))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2768))\)\(^{\oplus 1}\)