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Properties

Label 136.3
Level 136
Weight 3
Dimension 614
Nonzero newspaces 6
Newform subspaces 13
Sturm bound 3456
Trace bound 1

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Defining parameters

Level: \( N \) = \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 13 \)
Sturm bound: \(3456\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(136))\).

Total New Old
Modular forms 1248 674 574
Cusp forms 1056 614 442
Eisenstein series 192 60 132

Trace form

\( 614 q - 12 q^{2} - 12 q^{3} - 24 q^{4} - 24 q^{6} - 16 q^{7} - 22 q^{9} + O(q^{10}) \) \( 614 q - 12 q^{2} - 12 q^{3} - 24 q^{4} - 24 q^{6} - 16 q^{7} - 22 q^{9} - 16 q^{10} - 44 q^{11} - 16 q^{14} - 16 q^{15} - 48 q^{16} - 34 q^{17} - 52 q^{18} + 52 q^{19} - 16 q^{20} + 40 q^{22} - 16 q^{23} - 48 q^{24} + 78 q^{25} - 16 q^{26} + 72 q^{27} - 16 q^{28} + 80 q^{29} - 16 q^{30} + 48 q^{31} + 48 q^{32} + 24 q^{33} - 12 q^{34} - 96 q^{35} + 24 q^{36} - 128 q^{37} - 152 q^{38} - 208 q^{39} - 16 q^{40} - 100 q^{41} - 16 q^{42} - 284 q^{43} - 128 q^{44} - 240 q^{45} - 16 q^{46} - 16 q^{47} - 96 q^{48} - 130 q^{49} + 84 q^{50} - 12 q^{51} - 32 q^{52} - 168 q^{53} - 944 q^{54} - 592 q^{55} - 896 q^{56} - 408 q^{57} - 1024 q^{58} - 236 q^{59} - 1472 q^{60} - 288 q^{61} - 576 q^{62} - 592 q^{63} - 432 q^{64} - 56 q^{65} - 336 q^{66} - 156 q^{67} + 152 q^{68} + 192 q^{69} + 512 q^{70} + 176 q^{71} + 944 q^{72} + 324 q^{73} + 656 q^{74} + 1236 q^{75} + 1264 q^{76} + 480 q^{77} + 2272 q^{78} + 560 q^{79} + 1440 q^{80} + 326 q^{81} + 1000 q^{82} + 580 q^{83} + 1344 q^{84} + 728 q^{85} + 24 q^{86} + 656 q^{87} + 208 q^{88} + 252 q^{89} + 384 q^{90} + 624 q^{91} - 16 q^{92} + 512 q^{93} - 16 q^{94} + 464 q^{95} - 144 q^{96} + 284 q^{97} + 180 q^{98} + 124 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(136))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
136.3.d \(\chi_{136}(103, \cdot)\) None 0 1
136.3.e \(\chi_{136}(67, \cdot)\) 136.3.e.a 2 1
136.3.e.b 2
136.3.e.c 2
136.3.e.d 28
136.3.f \(\chi_{136}(35, \cdot)\) 136.3.f.a 32 1
136.3.g \(\chi_{136}(135, \cdot)\) None 0 1
136.3.j \(\chi_{136}(115, \cdot)\) 136.3.j.a 4 2
136.3.j.b 64
136.3.l \(\chi_{136}(47, \cdot)\) None 0 2
136.3.m \(\chi_{136}(15, \cdot)\) None 0 4
136.3.p \(\chi_{136}(19, \cdot)\) 136.3.p.a 4 4
136.3.p.b 4
136.3.p.c 128
136.3.q \(\chi_{136}(5, \cdot)\) 136.3.q.a 272 8
136.3.t \(\chi_{136}(41, \cdot)\) 136.3.t.a 32 8
136.3.t.b 40

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(136))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(136)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)