Properties

Label 24.2
Level 24
Weight 2
Dimension 5
Nonzero newspaces 3
Newforms 3
Sturm bound 64
Trace bound 2

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 3 \)
Sturm bound: \(64\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(24))\).

Total New Old
Modular forms 28 9 19
Cusp forms 5 5 0
Eisenstein series 23 4 19

Trace form

\(5q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 6q^{15} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut -\mathstrut 8q^{20} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut -\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 8q^{32} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 20q^{34} \) \(\mathstrut +\mathstrut 4q^{36} \) \(\mathstrut +\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut +\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut -\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut 24q^{47} \) \(\mathstrut -\mathstrut 8q^{48} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 18q^{51} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 6q^{54} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 12q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 4q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 16q^{64} \) \(\mathstrut +\mathstrut 20q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 12q^{72} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut -\mathstrut 24q^{76} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut +\mathstrut 12q^{79} \) \(\mathstrut -\mathstrut 11q^{81} \) \(\mathstrut -\mathstrut 36q^{82} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 8q^{84} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 8q^{86} \) \(\mathstrut -\mathstrut 18q^{87} \) \(\mathstrut +\mathstrut 16q^{88} \) \(\mathstrut -\mathstrut 26q^{89} \) \(\mathstrut -\mathstrut 4q^{90} \) \(\mathstrut -\mathstrut 8q^{93} \) \(\mathstrut +\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 8q^{95} \) \(\mathstrut +\mathstrut 24q^{96} \) \(\mathstrut -\mathstrut 22q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut -\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)

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
24.2.a \(\chi_{24}(1, \cdot)\) 24.2.a.a 1 1
24.2.c \(\chi_{24}(23, \cdot)\) None 0 1
24.2.d \(\chi_{24}(13, \cdot)\) 24.2.d.a 2 1
24.2.f \(\chi_{24}(11, \cdot)\) 24.2.f.a 2 1