Properties

Label 28.2
Level 28
Weight 2
Dimension 8
Nonzero newspaces 3
Newforms 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: \( 3 \)
Newforms: \( 3 \)
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

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

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 the 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

\( S_{2}^{\mathrm{old}}(\Gamma_1(28)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)