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Properties

Label 136.2
Level 136
Weight 2
Dimension 292
Nonzero newspaces 9
Newform subspaces 21
Sturm bound 2304
Trace bound 4

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Defining parameters

Level: \( N \) = \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 21 \)
Sturm bound: \(2304\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(136))\).

Total New Old
Modular forms 672 352 320
Cusp forms 481 292 189
Eisenstein series 191 60 131

Trace form

\( 292 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 32 q^{9} + O(q^{10}) \) \( 292 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 32 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 32 q^{17} - 32 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 52 q^{25} - 16 q^{26} - 40 q^{27} - 16 q^{28} - 20 q^{29} - 16 q^{30} - 48 q^{31} - 16 q^{32} - 64 q^{33} - 16 q^{34} - 64 q^{35} - 16 q^{36} - 32 q^{37} - 16 q^{38} - 48 q^{39} - 16 q^{40} - 52 q^{41} - 16 q^{42} - 40 q^{43} - 16 q^{44} - 20 q^{45} - 16 q^{46} - 16 q^{47} + 32 q^{48} - 32 q^{49} - 16 q^{50} - 16 q^{51} - 32 q^{52} + 12 q^{53} + 64 q^{54} + 32 q^{55} + 64 q^{56} - 8 q^{57} + 96 q^{58} + 32 q^{59} + 192 q^{60} + 48 q^{61} + 96 q^{62} + 128 q^{63} + 80 q^{64} - 20 q^{65} + 192 q^{66} + 48 q^{67} + 160 q^{68} + 96 q^{69} + 160 q^{70} + 32 q^{71} + 192 q^{72} - 20 q^{73} + 80 q^{74} + 128 q^{75} + 96 q^{76} + 48 q^{77} + 192 q^{78} + 32 q^{79} + 96 q^{80} - 8 q^{81} + 64 q^{82} + 24 q^{83} + 64 q^{84} - 20 q^{85} - 32 q^{86} - 64 q^{87} - 16 q^{88} - 80 q^{89} + 64 q^{90} - 80 q^{91} - 16 q^{92} - 64 q^{93} - 16 q^{94} - 96 q^{95} - 16 q^{96} - 64 q^{97} - 16 q^{98} - 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)

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
136.2.a \(\chi_{136}(1, \cdot)\) 136.2.a.a 1 1
136.2.a.b 1
136.2.a.c 2
136.2.b \(\chi_{136}(33, \cdot)\) 136.2.b.a 2 1
136.2.b.b 2
136.2.c \(\chi_{136}(69, \cdot)\) 136.2.c.a 8 1
136.2.c.b 8
136.2.h \(\chi_{136}(101, \cdot)\) 136.2.h.a 16 1
136.2.i \(\chi_{136}(13, \cdot)\) 136.2.i.a 8 2
136.2.i.b 24
136.2.k \(\chi_{136}(81, \cdot)\) 136.2.k.a 2 2
136.2.k.b 2
136.2.k.c 2
136.2.k.d 2
136.2.n \(\chi_{136}(9, \cdot)\) 136.2.n.a 4 4
136.2.n.b 4
136.2.n.c 12
136.2.o \(\chi_{136}(53, \cdot)\) 136.2.o.a 64 4
136.2.r \(\chi_{136}(7, \cdot)\) None 0 8
136.2.s \(\chi_{136}(3, \cdot)\) 136.2.s.a 8 8
136.2.s.b 8
136.2.s.c 112

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(136))\) into lower level spaces

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