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Properties

Label 604.2
Level 604
Weight 2
Dimension 6500
Nonzero newspaces 12
Newform subspaces 17
Sturm bound 45600
Trace bound 1

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Defining parameters

Level: \( N \) = \( 604 = 2^{2} \cdot 151 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 17 \)
Sturm bound: \(45600\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(604))\).

Total New Old
Modular forms 11775 6800 4975
Cusp forms 11026 6500 4526
Eisenstein series 749 300 449

Trace form

\( 6500 q - 75 q^{2} - 75 q^{4} - 150 q^{5} - 75 q^{6} - 75 q^{8} - 150 q^{9} + O(q^{10}) \) \( 6500 q - 75 q^{2} - 75 q^{4} - 150 q^{5} - 75 q^{6} - 75 q^{8} - 150 q^{9} - 75 q^{10} - 75 q^{12} - 150 q^{13} - 75 q^{14} - 75 q^{16} - 150 q^{17} - 75 q^{18} - 75 q^{20} - 150 q^{21} - 75 q^{22} - 75 q^{24} - 150 q^{25} - 75 q^{26} - 75 q^{28} - 150 q^{29} - 75 q^{30} - 75 q^{32} - 150 q^{33} - 75 q^{34} - 75 q^{36} - 150 q^{37} - 75 q^{38} - 75 q^{40} - 150 q^{41} - 75 q^{42} - 75 q^{44} - 150 q^{45} - 75 q^{46} - 75 q^{48} - 150 q^{49} - 75 q^{50} - 75 q^{52} - 150 q^{53} - 75 q^{54} - 75 q^{56} - 150 q^{57} - 75 q^{58} - 75 q^{60} - 150 q^{61} - 75 q^{62} - 75 q^{64} - 150 q^{65} - 75 q^{66} - 75 q^{68} - 150 q^{69} - 75 q^{70} - 75 q^{72} - 150 q^{73} - 75 q^{74} - 75 q^{76} - 150 q^{77} - 75 q^{78} - 75 q^{80} - 150 q^{81} - 75 q^{82} - 75 q^{84} - 150 q^{85} - 75 q^{86} - 75 q^{88} - 150 q^{89} - 75 q^{90} - 75 q^{92} - 150 q^{93} - 75 q^{94} - 75 q^{96} - 150 q^{97} - 75 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(604))\)

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
604.2.a \(\chi_{604}(1, \cdot)\) 604.2.a.a 3 1
604.2.a.b 3
604.2.a.c 6
604.2.d \(\chi_{604}(603, \cdot)\) 604.2.d.a 14 1
604.2.d.b 24
604.2.d.c 36
604.2.e \(\chi_{604}(269, \cdot)\) 604.2.e.a 26 2
604.2.f \(\chi_{604}(321, \cdot)\) 604.2.f.a 48 4
604.2.i \(\chi_{604}(119, \cdot)\) 604.2.i.a 4 2
604.2.i.b 144
604.2.j \(\chi_{604}(87, \cdot)\) 604.2.j.a 296 4
604.2.m \(\chi_{604}(85, \cdot)\) 604.2.m.a 104 8
604.2.n \(\chi_{604}(9, \cdot)\) 604.2.n.a 240 20
604.2.o \(\chi_{604}(23, \cdot)\) 604.2.o.a 592 8
604.2.s \(\chi_{604}(3, \cdot)\) 604.2.s.a 1480 20
604.2.u \(\chi_{604}(5, \cdot)\) 604.2.u.a 520 40
604.2.x \(\chi_{604}(7, \cdot)\) 604.2.x.a 2960 40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(604))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(604)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(151))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(302))\)\(^{\oplus 2}\)