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Properties

Label 1077.2
Level 1077
Weight 2
Dimension 31861
Nonzero newspaces 4
Sturm bound 171840
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1077 = 3 \cdot 359 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(171840\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1077))\).

Total New Old
Modular forms 43676 32577 11099
Cusp forms 42245 31861 10384
Eisenstein series 1431 716 715

Trace form

\( 31861 q - 3 q^{2} - 180 q^{3} - 365 q^{4} - 6 q^{5} - 182 q^{6} - 366 q^{7} - 15 q^{8} - 180 q^{9} + O(q^{10}) \) \( 31861 q - 3 q^{2} - 180 q^{3} - 365 q^{4} - 6 q^{5} - 182 q^{6} - 366 q^{7} - 15 q^{8} - 180 q^{9} - 376 q^{10} - 12 q^{11} - 186 q^{12} - 372 q^{13} - 24 q^{14} - 185 q^{15} - 389 q^{16} - 18 q^{17} - 182 q^{18} - 378 q^{19} - 42 q^{20} - 187 q^{21} - 394 q^{22} - 24 q^{23} - 194 q^{24} - 389 q^{25} - 42 q^{26} - 180 q^{27} - 414 q^{28} - 30 q^{29} - 197 q^{30} - 390 q^{31} - 63 q^{32} - 191 q^{33} - 412 q^{34} - 48 q^{35} - 186 q^{36} - 396 q^{37} - 60 q^{38} - 193 q^{39} - 448 q^{40} - 42 q^{41} - 203 q^{42} - 402 q^{43} - 84 q^{44} - 185 q^{45} - 430 q^{46} - 48 q^{47} - 210 q^{48} - 415 q^{49} - 93 q^{50} - 197 q^{51} - 456 q^{52} - 54 q^{53} - 182 q^{54} - 430 q^{55} - 120 q^{56} - 199 q^{57} - 448 q^{58} - 60 q^{59} - 221 q^{60} - 420 q^{61} - 96 q^{62} - 187 q^{63} - 485 q^{64} - 84 q^{65} - 215 q^{66} - 426 q^{67} - 126 q^{68} - 203 q^{69} - 502 q^{70} - 72 q^{71} - 194 q^{72} - 432 q^{73} - 114 q^{74} - 210 q^{75} - 498 q^{76} - 96 q^{77} - 221 q^{78} - 438 q^{79} - 186 q^{80} - 180 q^{81} - 484 q^{82} - 84 q^{83} - 235 q^{84} - 466 q^{85} - 132 q^{86} - 209 q^{87} - 538 q^{88} - 90 q^{89} - 197 q^{90} - 470 q^{91} - 168 q^{92} - 211 q^{93} - 502 q^{94} - 120 q^{95} - 242 q^{96} - 456 q^{97} - 171 q^{98} - 191 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1077))\)

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
1077.2.a \(\chi_{1077}(1, \cdot)\) 1077.2.a.a 1 1
1077.2.a.b 1
1077.2.a.c 1
1077.2.a.d 2
1077.2.a.e 2
1077.2.a.f 2
1077.2.a.g 3
1077.2.a.h 6
1077.2.a.i 10
1077.2.a.j 15
1077.2.a.k 16
1077.2.b \(\chi_{1077}(1076, \cdot)\) n/a 118 1
1077.2.e \(\chi_{1077}(4, \cdot)\) n/a 10680 178
1077.2.h \(\chi_{1077}(14, \cdot)\) n/a 21004 178

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1077))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1077)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(359))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1077))\)\(^{\oplus 1}\)