↑

Properties

Label 1604.2
Level 1604
Weight 2
Dimension 46500
Nonzero newspaces 15
Sturm bound 321600
Trace bound 5

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 1604 = 2^{2} \cdot 401 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 15 \)
Sturm bound: \(321600\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1604))\).

Total New Old
Modular forms 81400 47300 34100
Cusp forms 79401 46500 32901
Eisenstein series 1999 800 1199

Trace form

\( 46500 q - 200 q^{2} - 200 q^{4} - 400 q^{5} - 200 q^{6} - 200 q^{8} - 400 q^{9} + O(q^{10}) \) \( 46500 q - 200 q^{2} - 200 q^{4} - 400 q^{5} - 200 q^{6} - 200 q^{8} - 400 q^{9} - 200 q^{10} - 200 q^{12} - 400 q^{13} - 200 q^{14} - 200 q^{16} - 400 q^{17} - 200 q^{18} - 200 q^{20} - 400 q^{21} - 200 q^{22} - 200 q^{24} - 400 q^{25} - 200 q^{26} - 200 q^{28} - 400 q^{29} - 200 q^{30} - 200 q^{32} - 400 q^{33} - 200 q^{34} - 200 q^{36} - 400 q^{37} - 200 q^{38} - 200 q^{40} - 400 q^{41} - 200 q^{42} - 200 q^{44} - 400 q^{45} - 200 q^{46} - 200 q^{48} - 400 q^{49} - 200 q^{50} - 200 q^{52} - 400 q^{53} - 200 q^{54} - 200 q^{56} - 400 q^{57} - 200 q^{58} - 200 q^{60} - 400 q^{61} - 200 q^{62} - 200 q^{64} - 400 q^{65} - 200 q^{66} - 200 q^{68} - 400 q^{69} - 200 q^{70} - 200 q^{72} - 400 q^{73} - 200 q^{74} - 200 q^{76} - 400 q^{77} - 200 q^{78} - 200 q^{80} - 400 q^{81} - 200 q^{82} - 200 q^{84} - 400 q^{85} - 200 q^{86} - 200 q^{88} - 400 q^{89} - 200 q^{90} - 200 q^{92} - 400 q^{93} - 200 q^{94} - 200 q^{96} - 400 q^{97} - 200 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1604))\)

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
1604.2.a \(\chi_{1604}(1, \cdot)\) 1604.2.a.a 12 1
1604.2.a.b 22
1604.2.c \(\chi_{1604}(801, \cdot)\) 1604.2.c.a 34 1
1604.2.e \(\chi_{1604}(381, \cdot)\) 1604.2.e.a 68 2
1604.2.g \(\chi_{1604}(473, \cdot)\) n/a 136 4
1604.2.i \(\chi_{1604}(45, \cdot)\) n/a 132 4
1604.2.k \(\chi_{1604}(29, \cdot)\) n/a 136 4
1604.2.m \(\chi_{1604}(147, \cdot)\) n/a 1592 8
1604.2.p \(\chi_{1604}(237, \cdot)\) n/a 272 8
1604.2.q \(\chi_{1604}(5, \cdot)\) n/a 680 20
1604.2.s \(\chi_{1604}(213, \cdot)\) n/a 528 16
1604.2.u \(\chi_{1604}(41, \cdot)\) n/a 680 20
1604.2.w \(\chi_{1604}(119, \cdot)\) n/a 6368 32
1604.2.z \(\chi_{1604}(49, \cdot)\) n/a 1360 40
1604.2.ba \(\chi_{1604}(9, \cdot)\) n/a 2640 80
1604.2.bd \(\chi_{1604}(3, \cdot)\) n/a 31840 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1604))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1604)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(401))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(802))\)\(^{\oplus 2}\)