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Properties

Label 1336.2
Level 1336
Weight 2
Dimension 31042
Nonzero newspaces 6
Sturm bound 223104
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1336 = 2^{3} \cdot 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(223104\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1336))\).

Total New Old
Modular forms 56772 31702 25070
Cusp forms 54781 31042 23739
Eisenstein series 1991 660 1331

Trace form

\( 31042 q - 166 q^{2} - 166 q^{3} - 166 q^{4} - 166 q^{6} - 166 q^{7} - 166 q^{8} - 332 q^{9} + O(q^{10}) \) \( 31042 q - 166 q^{2} - 166 q^{3} - 166 q^{4} - 166 q^{6} - 166 q^{7} - 166 q^{8} - 332 q^{9} - 166 q^{10} - 166 q^{11} - 166 q^{12} - 166 q^{14} - 166 q^{15} - 166 q^{16} - 332 q^{17} - 166 q^{18} - 166 q^{19} - 166 q^{20} - 166 q^{22} - 166 q^{23} - 166 q^{24} - 332 q^{25} - 166 q^{26} - 166 q^{27} - 166 q^{28} - 166 q^{30} - 166 q^{31} - 166 q^{32} - 332 q^{33} - 166 q^{34} - 166 q^{35} - 166 q^{36} - 166 q^{38} - 166 q^{39} - 166 q^{40} - 332 q^{41} - 166 q^{42} - 166 q^{43} - 166 q^{44} - 166 q^{46} - 166 q^{47} - 166 q^{48} - 332 q^{49} - 166 q^{50} - 166 q^{51} - 166 q^{52} - 166 q^{54} - 166 q^{55} - 166 q^{56} - 332 q^{57} - 166 q^{58} - 166 q^{59} - 166 q^{60} - 166 q^{62} - 166 q^{63} - 166 q^{64} - 332 q^{65} - 166 q^{66} - 166 q^{67} - 166 q^{68} - 166 q^{70} - 166 q^{71} - 166 q^{72} - 332 q^{73} - 166 q^{74} - 166 q^{75} - 166 q^{76} - 166 q^{78} - 166 q^{79} - 166 q^{80} - 332 q^{81} - 166 q^{82} - 166 q^{83} - 166 q^{84} - 166 q^{86} - 166 q^{87} - 166 q^{88} - 332 q^{89} - 166 q^{90} - 166 q^{91} - 166 q^{92} - 166 q^{94} - 166 q^{95} - 166 q^{96} - 332 q^{97} - 166 q^{98} - 166 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1336))\)

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
1336.2.a \(\chi_{1336}(1, \cdot)\) 1336.2.a.a 2 1
1336.2.a.b 7
1336.2.a.c 9
1336.2.a.d 12
1336.2.a.e 12
1336.2.b \(\chi_{1336}(1335, \cdot)\) None 0 1
1336.2.c \(\chi_{1336}(669, \cdot)\) n/a 166 1
1336.2.h \(\chi_{1336}(667, \cdot)\) n/a 166 1
1336.2.i \(\chi_{1336}(9, \cdot)\) n/a 3444 82
1336.2.j \(\chi_{1336}(35, \cdot)\) n/a 13612 82
1336.2.o \(\chi_{1336}(21, \cdot)\) n/a 13612 82
1336.2.p \(\chi_{1336}(15, \cdot)\) None 0 82

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1336))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1336)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)\(^{\oplus 2}\)