Properties

Label 261.3
Level 261
Weight 3
Dimension 3860
Nonzero newspaces 12
Newform subspaces 17
Sturm bound 15120
Trace bound 4

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Defining parameters

Level: \( N \) = \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 17 \)
Sturm bound: \(15120\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(261))\).

Total New Old
Modular forms 5264 4104 1160
Cusp forms 4816 3860 956
Eisenstein series 448 244 204

Trace form

\( 3860 q - 36 q^{2} - 50 q^{3} - 40 q^{4} - 54 q^{5} - 74 q^{6} - 38 q^{7} - 42 q^{8} - 38 q^{9} + O(q^{10}) \) \( 3860 q - 36 q^{2} - 50 q^{3} - 40 q^{4} - 54 q^{5} - 74 q^{6} - 38 q^{7} - 42 q^{8} - 38 q^{9} - 102 q^{10} - 36 q^{11} - 68 q^{12} - 50 q^{13} - 54 q^{14} - 56 q^{15} - 64 q^{16} - 42 q^{17} - 56 q^{18} - 170 q^{19} + 138 q^{20} - 44 q^{21} + 120 q^{22} + 124 q^{23} + 34 q^{24} + 68 q^{25} + 28 q^{26} - 164 q^{27} - 120 q^{28} - 148 q^{29} - 148 q^{30} - 62 q^{31} - 320 q^{32} - 74 q^{33} - 198 q^{34} - 238 q^{35} - 38 q^{36} - 116 q^{37} - 256 q^{38} - 8 q^{39} - 354 q^{40} - 56 q^{42} - 164 q^{43} + 140 q^{44} + 52 q^{45} + 452 q^{46} + 406 q^{47} - 122 q^{48} + 316 q^{49} + 566 q^{50} - 218 q^{51} + 510 q^{52} + 210 q^{53} + 106 q^{54} + 122 q^{55} - 52 q^{56} + 10 q^{57} - 132 q^{58} - 314 q^{59} - 92 q^{60} - 154 q^{61} - 532 q^{62} - 128 q^{63} - 724 q^{64} - 594 q^{65} - 20 q^{66} - 664 q^{67} - 1066 q^{68} - 56 q^{69} - 2866 q^{70} - 2324 q^{71} - 2678 q^{72} - 2038 q^{73} - 3508 q^{74} - 1518 q^{75} - 3380 q^{76} - 1944 q^{77} - 1920 q^{78} - 554 q^{79} - 3570 q^{80} - 1014 q^{81} - 882 q^{82} - 378 q^{83} - 716 q^{84} - 186 q^{85} + 282 q^{86} + 318 q^{87} + 894 q^{88} + 588 q^{89} + 956 q^{90} + 1166 q^{91} + 2886 q^{92} + 344 q^{93} + 1134 q^{94} + 2850 q^{95} + 3864 q^{96} + 1534 q^{97} + 5180 q^{98} + 1764 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(261))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
261.3.b \(\chi_{261}(233, \cdot)\) 261.3.b.a 20 1
261.3.d \(\chi_{261}(260, \cdot)\) 261.3.d.a 20 1
261.3.f \(\chi_{261}(46, \cdot)\) 261.3.f.a 8 2
261.3.f.b 8
261.3.f.c 12
261.3.f.d 20
261.3.h \(\chi_{261}(86, \cdot)\) 261.3.h.a 116 2
261.3.j \(\chi_{261}(59, \cdot)\) 261.3.j.a 112 2
261.3.m \(\chi_{261}(70, \cdot)\) 261.3.m.a 232 4
261.3.n \(\chi_{261}(35, \cdot)\) 261.3.n.a 120 6
261.3.p \(\chi_{261}(53, \cdot)\) 261.3.p.a 120 6
261.3.s \(\chi_{261}(10, \cdot)\) 261.3.s.a 48 12
261.3.s.b 120
261.3.s.c 120
261.3.t \(\chi_{261}(20, \cdot)\) 261.3.t.a 696 12
261.3.v \(\chi_{261}(5, \cdot)\) 261.3.v.a 696 12
261.3.w \(\chi_{261}(31, \cdot)\) 261.3.w.a 1392 24

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(261))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(261)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 2}\)