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Properties

Label 266.2
Level 266
Weight 2
Dimension 689
Nonzero newspaces 16
Newform subspaces 37
Sturm bound 8640
Trace bound 7

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Defining parameters

Level: \( N \) = \( 266 = 2 \cdot 7 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 37 \)
Sturm bound: \(8640\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(266))\).

Total New Old
Modular forms 2376 689 1687
Cusp forms 1945 689 1256
Eisenstein series 431 0 431

Trace form

\( 689 q + 3 q^{2} + 8 q^{3} - q^{4} + 6 q^{5} - q^{7} + 3 q^{8} + 11 q^{9} + O(q^{10}) \) \( 689 q + 3 q^{2} + 8 q^{3} - q^{4} + 6 q^{5} - q^{7} + 3 q^{8} + 11 q^{9} + 6 q^{10} + 12 q^{11} - 4 q^{12} - 26 q^{13} - 15 q^{14} - 48 q^{15} - q^{16} - 30 q^{17} - 39 q^{18} - 67 q^{19} - 30 q^{20} - 34 q^{21} - 42 q^{22} - 12 q^{23} - 31 q^{25} - 30 q^{26} - 34 q^{27} - 7 q^{28} + 6 q^{29} + 24 q^{30} + 4 q^{31} + 3 q^{32} - 60 q^{33} + 30 q^{34} - 30 q^{35} + 11 q^{36} - 2 q^{37} + 21 q^{38} - 68 q^{39} + 6 q^{40} - 6 q^{41} - 56 q^{43} - 6 q^{44} - 138 q^{45} - 48 q^{46} - 72 q^{47} - 10 q^{48} - 19 q^{49} - 123 q^{50} - 102 q^{51} + 10 q^{52} - 102 q^{53} - 60 q^{54} - 72 q^{55} - 33 q^{56} - 100 q^{57} - 54 q^{58} - 108 q^{59} - 48 q^{60} - 110 q^{61} - 84 q^{62} - 85 q^{63} - 13 q^{64} - 132 q^{65} - 96 q^{66} - 80 q^{67} - 12 q^{68} - 12 q^{69} - 30 q^{70} - 72 q^{71} - 3 q^{72} + 4 q^{73} + 42 q^{74} + 20 q^{75} + 17 q^{76} - 24 q^{77} - 92 q^{79} + 6 q^{80} - 55 q^{81} - 18 q^{82} - 48 q^{83} - 46 q^{84} - 36 q^{85} - 12 q^{86} - 264 q^{87} + 12 q^{88} - 42 q^{89} - 102 q^{90} - 74 q^{91} - 48 q^{92} - 188 q^{93} - 120 q^{94} - 66 q^{95} - 62 q^{97} - 69 q^{98} - 258 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)

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
266.2.a \(\chi_{266}(1, \cdot)\) 266.2.a.a 2 1
266.2.a.b 2
266.2.a.c 2
266.2.a.d 3
266.2.d \(\chi_{266}(265, \cdot)\) 266.2.d.a 16 1
266.2.e \(\chi_{266}(39, \cdot)\) 266.2.e.a 2 2
266.2.e.b 2
266.2.e.c 4
266.2.e.d 6
266.2.e.e 10
266.2.f \(\chi_{266}(197, \cdot)\) 266.2.f.a 2 2
266.2.f.b 4
266.2.f.c 6
266.2.f.d 8
266.2.g \(\chi_{266}(11, \cdot)\) 266.2.g.a 2 2
266.2.g.b 10
266.2.g.c 12
266.2.h \(\chi_{266}(163, \cdot)\) 266.2.h.a 2 2
266.2.h.b 10
266.2.h.c 12
266.2.k \(\chi_{266}(145, \cdot)\) 266.2.k.a 4 2
266.2.k.b 20
266.2.l \(\chi_{266}(75, \cdot)\) 266.2.l.a 24 2
266.2.m \(\chi_{266}(27, \cdot)\) 266.2.m.a 32 2
266.2.t \(\chi_{266}(31, \cdot)\) 266.2.t.a 4 2
266.2.t.b 20
266.2.u \(\chi_{266}(43, \cdot)\) 266.2.u.a 6 6
266.2.u.b 12
266.2.u.c 18
266.2.u.d 24
266.2.v \(\chi_{266}(9, \cdot)\) 266.2.v.a 42 6
266.2.v.b 42
266.2.w \(\chi_{266}(25, \cdot)\) 266.2.w.a 42 6
266.2.w.b 42
266.2.x \(\chi_{266}(13, \cdot)\) 266.2.x.a 72 6
266.2.y \(\chi_{266}(3, \cdot)\) 266.2.y.a 84 6
266.2.bd \(\chi_{266}(33, \cdot)\) 266.2.bd.a 84 6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(266))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(266)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 2}\)