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Properties

Label 28.2
Level 28
Weight 2
Dimension 8
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 96
Trace bound 2

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Defining parameters

Level: \( N \) = \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(28))\).

Total New Old
Modular forms 39 20 19
Cusp forms 10 8 2
Eisenstein series 29 12 17

Trace form

\( 8 q - 3 q^{2} - q^{3} - 3 q^{4} - 9 q^{5} - 4 q^{7} - 3 q^{8} - 4 q^{9} + O(q^{10}) \) \( 8 q - 3 q^{2} - q^{3} - 3 q^{4} - 9 q^{5} - 4 q^{7} - 3 q^{8} - 4 q^{9} + 6 q^{10} + 3 q^{11} + 12 q^{12} + 4 q^{13} + 9 q^{14} + 6 q^{15} + 9 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 5 q^{21} - 18 q^{22} - 3 q^{23} - 12 q^{24} + 2 q^{25} - 12 q^{26} - 10 q^{27} - 27 q^{28} - 6 q^{30} + 7 q^{31} - 3 q^{32} + 9 q^{33} + 15 q^{35} + 9 q^{36} + 7 q^{37} + 18 q^{38} - 2 q^{39} + 12 q^{40} + 12 q^{41} + 12 q^{42} - 8 q^{43} + 18 q^{44} + 6 q^{45} + 12 q^{46} + 9 q^{47} - 16 q^{49} + 3 q^{50} - 3 q^{51} - 21 q^{53} - 18 q^{54} - 18 q^{55} + 9 q^{56} - 38 q^{57} - 6 q^{58} - 9 q^{59} - 12 q^{60} - 17 q^{61} - 10 q^{63} + 9 q^{64} + 6 q^{65} - 6 q^{66} + 7 q^{67} + 6 q^{69} + 6 q^{70} - 15 q^{72} + 31 q^{73} - 12 q^{74} - 4 q^{75} + 21 q^{77} + 24 q^{78} + 13 q^{79} - 24 q^{80} + 35 q^{81} + 12 q^{82} + 24 q^{83} + 30 q^{85} - 18 q^{86} + 6 q^{87} + 18 q^{88} + 39 q^{89} - 8 q^{91} - 6 q^{92} + 13 q^{93} - 30 q^{94} + 3 q^{95} - 24 q^{96} - 20 q^{97} - 15 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)

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
28.2.a \(\chi_{28}(1, \cdot)\) None 0 1
28.2.d \(\chi_{28}(27, \cdot)\) 28.2.d.a 2 1
28.2.e \(\chi_{28}(9, \cdot)\) 28.2.e.a 2 2
28.2.f \(\chi_{28}(3, \cdot)\) 28.2.f.a 4 2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(28))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(28)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 1}\)