Properties

Label 266.4
Level 266
Weight 4
Dimension 2058
Nonzero newspaces 16
Sturm bound 17280
Trace bound 11

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Defining parameters

Level: \( N \) = \( 266 = 2 \cdot 7 \cdot 19 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(17280\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(266))\).

Total New Old
Modular forms 6696 2058 4638
Cusp forms 6264 2058 4206
Eisenstein series 432 0 432

Trace form

\( 2058 q - 24 q^{3} + 48 q^{5} + 72 q^{6} + 96 q^{7} - 84 q^{9} + O(q^{10}) \) \( 2058 q - 24 q^{3} + 48 q^{5} + 72 q^{6} + 96 q^{7} - 84 q^{9} - 72 q^{10} - 84 q^{11} - 384 q^{12} - 708 q^{13} - 300 q^{14} + 456 q^{15} + 876 q^{17} + 1308 q^{18} + 1572 q^{19} + 816 q^{20} + 648 q^{21} + 756 q^{22} + 516 q^{23} + 96 q^{24} - 2148 q^{25} - 2064 q^{26} - 5058 q^{27} - 672 q^{28} - 2412 q^{29} - 336 q^{30} - 600 q^{31} + 2976 q^{33} + 816 q^{34} + 1956 q^{35} + 336 q^{36} + 1248 q^{37} - 108 q^{38} + 4284 q^{39} - 288 q^{40} + 2484 q^{41} - 648 q^{42} + 24 q^{43} - 2136 q^{44} - 10104 q^{45} - 3552 q^{46} - 5544 q^{47} - 96 q^{48} - 1530 q^{49} + 1968 q^{50} - 198 q^{51} - 192 q^{52} + 3732 q^{53} + 5688 q^{54} + 5112 q^{55} + 1920 q^{56} + 9768 q^{57} + 4896 q^{58} + 9528 q^{59} + 4176 q^{60} + 1884 q^{61} + 2568 q^{62} - 840 q^{63} - 768 q^{64} - 108 q^{65} - 4128 q^{66} - 204 q^{67} - 168 q^{68} - 8136 q^{69} - 3024 q^{70} - 13068 q^{71} - 1968 q^{72} + 2322 q^{73} - 3024 q^{74} + 5832 q^{75} - 1464 q^{76} - 6954 q^{77} - 15120 q^{78} - 7320 q^{79} + 768 q^{80} - 10410 q^{81} - 2496 q^{82} - 3408 q^{83} + 960 q^{84} + 96 q^{85} - 96 q^{86} + 2232 q^{87} - 2688 q^{88} - 1560 q^{89} + 8544 q^{90} + 132 q^{91} + 7200 q^{92} + 23136 q^{93} + 15168 q^{94} - 4278 q^{95} + 384 q^{96} + 6504 q^{97} + 11184 q^{98} + 16554 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(266))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
266.4.a \(\chi_{266}(1, \cdot)\) 266.4.a.a 2 1
266.4.a.b 2
266.4.a.c 2
266.4.a.d 2
266.4.a.e 4
266.4.a.f 4
266.4.a.g 5
266.4.a.h 5
266.4.d \(\chi_{266}(265, \cdot)\) 266.4.d.a 40 1
266.4.e \(\chi_{266}(39, \cdot)\) 266.4.e.a 14 2
266.4.e.b 16
266.4.e.c 20
266.4.e.d 22
266.4.f \(\chi_{266}(197, \cdot)\) 266.4.f.a 2 2
266.4.f.b 12
266.4.f.c 12
266.4.f.d 16
266.4.f.e 18
266.4.g \(\chi_{266}(11, \cdot)\) 266.4.g.a 2 2
266.4.g.b 38
266.4.g.c 40
266.4.h \(\chi_{266}(163, \cdot)\) 266.4.h.a 2 2
266.4.h.b 38
266.4.h.c 40
266.4.k \(\chi_{266}(145, \cdot)\) 266.4.k.a 80 2
266.4.l \(\chi_{266}(75, \cdot)\) 266.4.l.a 80 2
266.4.m \(\chi_{266}(27, \cdot)\) 266.4.m.a 80 2
266.4.t \(\chi_{266}(31, \cdot)\) 266.4.t.a 80 2
266.4.u \(\chi_{266}(43, \cdot)\) n/a 180 6
266.4.v \(\chi_{266}(9, \cdot)\) n/a 240 6
266.4.w \(\chi_{266}(25, \cdot)\) n/a 240 6
266.4.x \(\chi_{266}(13, \cdot)\) n/a 240 6
266.4.y \(\chi_{266}(3, \cdot)\) n/a 240 6
266.4.bd \(\chi_{266}(33, \cdot)\) n/a 240 6

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(266))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(266)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 2}\)