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Properties

Label 2012.2
Level 2012
Weight 2
Dimension 73292
Nonzero newspaces 4
Sturm bound 506016
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2012 = 2^{2} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(506016\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2012))\).

Total New Old
Modular forms 127759 74296 53463
Cusp forms 125250 73292 51958
Eisenstein series 2509 1004 1505

Trace form

\( 73292 q - 251 q^{2} - 251 q^{4} - 502 q^{5} - 251 q^{6} - 251 q^{8} - 502 q^{9} + O(q^{10}) \) \( 73292 q - 251 q^{2} - 251 q^{4} - 502 q^{5} - 251 q^{6} - 251 q^{8} - 502 q^{9} - 251 q^{10} - 251 q^{12} - 502 q^{13} - 251 q^{14} - 251 q^{16} - 502 q^{17} - 251 q^{18} - 251 q^{20} - 502 q^{21} - 251 q^{22} - 251 q^{24} - 502 q^{25} - 251 q^{26} - 251 q^{28} - 502 q^{29} - 251 q^{30} - 251 q^{32} - 502 q^{33} - 251 q^{34} - 251 q^{36} - 502 q^{37} - 251 q^{38} - 251 q^{40} - 502 q^{41} - 251 q^{42} - 251 q^{44} - 502 q^{45} - 251 q^{46} - 251 q^{48} - 502 q^{49} - 251 q^{50} - 251 q^{52} - 502 q^{53} - 251 q^{54} - 251 q^{56} - 502 q^{57} - 251 q^{58} - 251 q^{60} - 502 q^{61} - 251 q^{62} - 251 q^{64} - 502 q^{65} - 251 q^{66} - 251 q^{68} - 502 q^{69} - 251 q^{70} - 251 q^{72} - 502 q^{73} - 251 q^{74} - 251 q^{76} - 502 q^{77} - 251 q^{78} - 251 q^{80} - 502 q^{81} - 251 q^{82} - 251 q^{84} - 502 q^{85} - 251 q^{86} - 251 q^{88} - 502 q^{89} - 251 q^{90} - 251 q^{92} - 502 q^{93} - 251 q^{94} - 251 q^{96} - 502 q^{97} - 251 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2012))\)

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
2012.2.a \(\chi_{2012}(1, \cdot)\) 2012.2.a.a 21 1
2012.2.a.b 21
2012.2.b \(\chi_{2012}(2011, \cdot)\) n/a 250 1
2012.2.e \(\chi_{2012}(9, \cdot)\) n/a 10500 250
2012.2.h \(\chi_{2012}(15, \cdot)\) n/a 62500 250

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2012))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(503))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1006))\)\(^{\oplus 2}\)