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Properties

Label 548.2
Level 548
Weight 2
Dimension 5338
Nonzero newspaces 8
Newform subspaces 11
Sturm bound 37536
Trace bound 5

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Defining parameters

Level: \( N \) = \( 548 = 2^{2} \cdot 137 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 11 \)
Sturm bound: \(37536\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(548))\).

Total New Old
Modular forms 9724 5610 4114
Cusp forms 9045 5338 3707
Eisenstein series 679 272 407

Trace form

\( 5338 q - 68 q^{2} - 68 q^{4} - 136 q^{5} - 68 q^{6} - 68 q^{8} - 136 q^{9} + O(q^{10}) \) \( 5338 q - 68 q^{2} - 68 q^{4} - 136 q^{5} - 68 q^{6} - 68 q^{8} - 136 q^{9} - 68 q^{10} - 68 q^{12} - 136 q^{13} - 68 q^{14} - 68 q^{16} - 136 q^{17} - 68 q^{18} - 68 q^{20} - 136 q^{21} - 68 q^{22} - 68 q^{24} - 136 q^{25} - 68 q^{26} - 68 q^{28} - 136 q^{29} - 68 q^{30} - 68 q^{32} - 136 q^{33} - 68 q^{34} - 68 q^{36} - 136 q^{37} - 68 q^{38} - 68 q^{40} - 136 q^{41} - 68 q^{42} - 68 q^{44} - 136 q^{45} - 68 q^{46} - 68 q^{48} - 136 q^{49} - 68 q^{50} - 68 q^{52} - 136 q^{53} - 68 q^{54} - 68 q^{56} - 136 q^{57} - 68 q^{58} - 68 q^{60} - 136 q^{61} - 68 q^{62} - 68 q^{64} - 136 q^{65} - 68 q^{66} - 68 q^{68} - 136 q^{69} - 68 q^{70} - 68 q^{72} - 136 q^{73} - 68 q^{74} - 68 q^{76} - 136 q^{77} - 68 q^{78} - 68 q^{80} - 136 q^{81} - 68 q^{82} - 68 q^{84} - 136 q^{85} - 68 q^{86} - 68 q^{88} - 136 q^{89} - 68 q^{90} - 68 q^{92} - 136 q^{93} - 68 q^{94} - 68 q^{96} - 136 q^{97} - 68 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(548))\)

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
548.2.a \(\chi_{548}(1, \cdot)\) 548.2.a.a 4 1
548.2.a.b 8
548.2.b \(\chi_{548}(273, \cdot)\) 548.2.b.a 12 1
548.2.e \(\chi_{548}(37, \cdot)\) 548.2.e.a 22 2
548.2.h \(\chi_{548}(127, \cdot)\) 548.2.h.a 4 4
548.2.h.b 264
548.2.i \(\chi_{548}(73, \cdot)\) 548.2.i.a 192 16
548.2.l \(\chi_{548}(49, \cdot)\) 548.2.l.a 192 16
548.2.n \(\chi_{548}(9, \cdot)\) 548.2.n.a 352 32
548.2.o \(\chi_{548}(3, \cdot)\) 548.2.o.a 64 64
548.2.o.b 4224

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(548))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(548)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(137))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(274))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(548))\)\(^{\oplus 1}\)