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Properties

Label 212.2
Level 212
Weight 2
Dimension 767
Nonzero newspaces 6
Newform subspaces 10
Sturm bound 5616
Trace bound 1

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Defining parameters

Level: \( N \) = \( 212 = 2^{2} \cdot 53 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 10 \)
Sturm bound: \(5616\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(212))\).

Total New Old
Modular forms 1534 871 663
Cusp forms 1275 767 508
Eisenstein series 259 104 155

Trace form

\( 767 q - 26 q^{2} - 26 q^{4} - 52 q^{5} - 26 q^{6} - 26 q^{8} - 52 q^{9} + O(q^{10}) \) \( 767 q - 26 q^{2} - 26 q^{4} - 52 q^{5} - 26 q^{6} - 26 q^{8} - 52 q^{9} - 26 q^{10} - 26 q^{12} - 52 q^{13} - 26 q^{14} - 26 q^{16} - 52 q^{17} - 26 q^{18} - 26 q^{20} - 52 q^{21} - 26 q^{22} - 26 q^{24} - 52 q^{25} - 26 q^{26} - 26 q^{28} - 52 q^{29} - 26 q^{30} - 26 q^{32} - 52 q^{33} - 26 q^{34} - 26 q^{36} - 52 q^{37} - 26 q^{38} - 26 q^{40} - 78 q^{41} - 26 q^{42} - 52 q^{43} - 26 q^{44} - 182 q^{45} - 26 q^{46} - 26 q^{47} - 26 q^{48} - 104 q^{49} - 26 q^{50} - 104 q^{51} - 130 q^{53} - 52 q^{54} - 78 q^{55} - 26 q^{56} - 156 q^{57} - 26 q^{58} - 52 q^{59} - 26 q^{60} - 78 q^{61} - 26 q^{62} - 130 q^{63} - 26 q^{64} - 104 q^{65} - 26 q^{66} - 26 q^{67} - 26 q^{68} - 52 q^{69} - 26 q^{70} - 26 q^{72} - 52 q^{73} - 26 q^{74} - 26 q^{76} - 52 q^{77} - 26 q^{78} - 26 q^{80} - 52 q^{81} - 26 q^{82} - 26 q^{84} - 52 q^{85} - 26 q^{86} + 52 q^{87} + 104 q^{88} + 13 q^{89} + 182 q^{90} + 104 q^{91} + 208 q^{92} + 52 q^{93} + 286 q^{94} + 104 q^{95} + 234 q^{96} + 169 q^{97} + 182 q^{98} + 260 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(212))\)

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
212.2.a \(\chi_{212}(1, \cdot)\) 212.2.a.a 1 1
212.2.a.b 1
212.2.a.c 3
212.2.b \(\chi_{212}(105, \cdot)\) 212.2.b.a 4 1
212.2.f \(\chi_{212}(23, \cdot)\) 212.2.f.a 2 2
212.2.f.b 48
212.2.g \(\chi_{212}(13, \cdot)\) 212.2.g.a 60 12
212.2.j \(\chi_{212}(9, \cdot)\) 212.2.j.a 48 12
212.2.k \(\chi_{212}(3, \cdot)\) 212.2.k.a 24 24
212.2.k.b 576

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(212))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(212)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(212))\)\(^{\oplus 1}\)