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Properties

Label 212.1
Level 212
Weight 1
Dimension 14
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 2808
Trace bound 1

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Defining parameters

Level: \( N \) = \( 212 = 2^{2} \cdot 53 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(2808\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(212))\).

Total New Old
Modular forms 144 64 80
Cusp forms 14 14 0
Eisenstein series 130 50 80

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 14 0 0 0

Trace form

\( 14 q - q^{2} + q^{4} - 2 q^{5} - 2 q^{6} - q^{8} - q^{9} + O(q^{10}) \) \( 14 q - q^{2} + q^{4} - 2 q^{5} - 2 q^{6} - q^{8} - q^{9} - 2 q^{10} - 4 q^{13} + q^{16} - 4 q^{17} - q^{18} - 2 q^{20} - 2 q^{24} - q^{25} - 2 q^{26} - 4 q^{29} - q^{32} - 2 q^{34} - q^{36} - 4 q^{37} - 2 q^{38} + 11 q^{40} - 2 q^{41} - 2 q^{45} - 2 q^{46} + q^{49} + 10 q^{50} - 4 q^{52} + q^{53} + 2 q^{54} + 2 q^{57} + 11 q^{58} - 2 q^{61} + 4 q^{62} + q^{64} - 4 q^{65} + 9 q^{68} + 2 q^{69} - q^{72} - 2 q^{73} - 2 q^{74} + 2 q^{78} - 2 q^{80} - 3 q^{81} - 2 q^{82} - 4 q^{85} + 15 q^{89} - 2 q^{90} - 4 q^{93} - 2 q^{96} + 9 q^{97} - q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(212))\)

We only show spaces with odd 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
212.1.c \(\chi_{212}(107, \cdot)\) None 0 1
212.1.d \(\chi_{212}(211, \cdot)\) 212.1.d.a 1 1
212.1.d.b 1
212.1.e \(\chi_{212}(129, \cdot)\) None 0 2
212.1.h \(\chi_{212}(7, \cdot)\) None 0 12
212.1.i \(\chi_{212}(15, \cdot)\) 212.1.i.a 12 12
212.1.l \(\chi_{212}(5, \cdot)\) None 0 24