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Properties

Label 261.2
Level 261
Weight 2
Dimension 1869
Nonzero newspaces 12
Newform subspaces 26
Sturm bound 10080
Trace bound 2

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Defining parameters

Level: \( N \) = \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 26 \)
Sturm bound: \(10080\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(261))\).

Total New Old
Modular forms 2744 2111 633
Cusp forms 2297 1869 428
Eisenstein series 447 242 205

Trace form

\( 1869 q - 42 q^{2} - 56 q^{3} - 42 q^{4} - 42 q^{5} - 56 q^{6} - 42 q^{7} - 42 q^{8} - 56 q^{9} + O(q^{10}) \) \( 1869 q - 42 q^{2} - 56 q^{3} - 42 q^{4} - 42 q^{5} - 56 q^{6} - 42 q^{7} - 42 q^{8} - 56 q^{9} - 126 q^{10} - 42 q^{11} - 56 q^{12} - 42 q^{13} - 42 q^{14} - 56 q^{15} - 42 q^{16} - 42 q^{17} - 56 q^{18} - 126 q^{19} - 63 q^{20} - 56 q^{21} - 70 q^{22} - 56 q^{23} - 56 q^{24} - 70 q^{25} - 77 q^{26} - 56 q^{27} - 196 q^{28} - 70 q^{29} - 112 q^{30} - 70 q^{31} - 98 q^{32} - 56 q^{33} - 77 q^{34} - 70 q^{35} - 56 q^{36} - 140 q^{37} - 70 q^{38} - 56 q^{39} - 63 q^{40} - 42 q^{41} - 56 q^{42} - 42 q^{43} - 56 q^{44} - 56 q^{45} - 196 q^{46} - 70 q^{47} - 56 q^{48} - 98 q^{49} - 140 q^{50} - 56 q^{51} - 154 q^{52} - 105 q^{53} - 56 q^{54} - 238 q^{55} - 56 q^{56} - 56 q^{57} - 210 q^{58} - 112 q^{59} - 56 q^{60} - 98 q^{61} - 140 q^{62} - 56 q^{63} - 252 q^{64} - 105 q^{65} - 56 q^{66} - 98 q^{67} - 140 q^{68} - 56 q^{69} - 70 q^{70} + 56 q^{71} + 112 q^{72} - 77 q^{73} + 196 q^{74} + 84 q^{75} + 294 q^{76} + 168 q^{77} + 168 q^{78} + 42 q^{79} + 546 q^{80} + 168 q^{81} + 42 q^{82} + 126 q^{83} + 280 q^{84} + 210 q^{85} + 420 q^{86} + 84 q^{87} + 420 q^{88} + 168 q^{89} + 224 q^{90} + 126 q^{91} + 462 q^{92} + 56 q^{93} + 126 q^{94} + 294 q^{95} + 336 q^{96} - 7 q^{97} + 224 q^{98} + 84 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)

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
261.2.a \(\chi_{261}(1, \cdot)\) 261.2.a.a 2 1
261.2.a.b 2
261.2.a.c 2
261.2.a.d 2
261.2.a.e 3
261.2.c \(\chi_{261}(28, \cdot)\) 261.2.c.a 2 1
261.2.c.b 4
261.2.c.c 6
261.2.e \(\chi_{261}(88, \cdot)\) 261.2.e.a 22 2
261.2.e.b 34
261.2.g \(\chi_{261}(17, \cdot)\) 261.2.g.a 4 2
261.2.g.b 8
261.2.g.c 8
261.2.i \(\chi_{261}(115, \cdot)\) 261.2.i.a 56 2
261.2.k \(\chi_{261}(82, \cdot)\) 261.2.k.a 6 6
261.2.k.b 18
261.2.k.c 18
261.2.k.d 24
261.2.l \(\chi_{261}(41, \cdot)\) 261.2.l.a 112 4
261.2.o \(\chi_{261}(64, \cdot)\) 261.2.o.a 12 6
261.2.o.b 24
261.2.o.c 36
261.2.q \(\chi_{261}(7, \cdot)\) 261.2.q.a 336 12
261.2.r \(\chi_{261}(8, \cdot)\) 261.2.r.a 120 12
261.2.u \(\chi_{261}(4, \cdot)\) 261.2.u.a 336 12
261.2.x \(\chi_{261}(2, \cdot)\) 261.2.x.a 672 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(261))\) into lower level spaces

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