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

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

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 the 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

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