Properties

Label 23.2
Level 23
Weight 2
Dimension 12
Nonzero newspaces 2
Newforms 2
Sturm bound 88
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
Sturm bound: \(88\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(23))\).

Total New Old
Modular forms 33 33 0
Cusp forms 12 12 0
Eisenstein series 21 21 0

Trace form

\(12q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut -\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut +\mathstrut 4q^{8} \) \(\mathstrut +\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut +\mathstrut 13q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 16q^{18} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 13q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 8q^{22} \) \(\mathstrut -\mathstrut 10q^{23} \) \(\mathstrut -\mathstrut 28q^{24} \) \(\mathstrut -\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut q^{28} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut +\mathstrut 10q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 21q^{34} \) \(\mathstrut +\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 25q^{36} \) \(\mathstrut -\mathstrut 17q^{37} \) \(\mathstrut -\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut -\mathstrut 9q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 25q^{42} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut -\mathstrut 26q^{44} \) \(\mathstrut -\mathstrut 10q^{45} \) \(\mathstrut -\mathstrut 30q^{46} \) \(\mathstrut -\mathstrut 18q^{47} \) \(\mathstrut +\mathstrut 3q^{48} \) \(\mathstrut -\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 17q^{51} \) \(\mathstrut -\mathstrut 23q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut -\mathstrut q^{54} \) \(\mathstrut -\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 12q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 20q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 25q^{60} \) \(\mathstrut +\mathstrut 7q^{61} \) \(\mathstrut +\mathstrut 19q^{62} \) \(\mathstrut +\mathstrut 38q^{63} \) \(\mathstrut +\mathstrut 28q^{64} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut +\mathstrut 12q^{66} \) \(\mathstrut +\mathstrut 35q^{67} \) \(\mathstrut -\mathstrut 28q^{68} \) \(\mathstrut +\mathstrut 26q^{69} \) \(\mathstrut +\mathstrut 34q^{70} \) \(\mathstrut +\mathstrut 6q^{71} \) \(\mathstrut +\mathstrut 19q^{72} \) \(\mathstrut +\mathstrut 41q^{73} \) \(\mathstrut +\mathstrut 4q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 14q^{76} \) \(\mathstrut -\mathstrut 14q^{77} \) \(\mathstrut -\mathstrut 19q^{78} \) \(\mathstrut -\mathstrut 19q^{79} \) \(\mathstrut -\mathstrut 34q^{80} \) \(\mathstrut -\mathstrut 66q^{81} \) \(\mathstrut +\mathstrut 5q^{82} \) \(\mathstrut -\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 7q^{84} \) \(\mathstrut -\mathstrut 35q^{85} \) \(\mathstrut -\mathstrut 11q^{86} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 37q^{88} \) \(\mathstrut +\mathstrut 13q^{89} \) \(\mathstrut -\mathstrut 8q^{90} \) \(\mathstrut +\mathstrut 2q^{91} \) \(\mathstrut +\mathstrut 51q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 12q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 12q^{97} \) \(\mathstrut +\mathstrut 28q^{98} \) \(\mathstrut -\mathstrut 42q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)

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
23.2.a \(\chi_{23}(1, \cdot)\) 23.2.a.a 2 1
23.2.c \(\chi_{23}(2, \cdot)\) 23.2.c.a 10 10