Properties

Label 229.2
Level 229
Weight 2
Dimension 2072
Nonzero newspaces 8
Newforms 12
Sturm bound 8740
Trace bound 3

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 229 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newforms: \( 12 \)
Sturm bound: \(8740\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(229))\).

Total New Old
Modular forms 2299 2299 0
Cusp forms 2072 2072 0
Eisenstein series 227 227 0

Trace form

\(2072q \) \(\mathstrut -\mathstrut 111q^{2} \) \(\mathstrut -\mathstrut 110q^{3} \) \(\mathstrut -\mathstrut 107q^{4} \) \(\mathstrut -\mathstrut 108q^{5} \) \(\mathstrut -\mathstrut 102q^{6} \) \(\mathstrut -\mathstrut 106q^{7} \) \(\mathstrut -\mathstrut 99q^{8} \) \(\mathstrut -\mathstrut 101q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2072q \) \(\mathstrut -\mathstrut 111q^{2} \) \(\mathstrut -\mathstrut 110q^{3} \) \(\mathstrut -\mathstrut 107q^{4} \) \(\mathstrut -\mathstrut 108q^{5} \) \(\mathstrut -\mathstrut 102q^{6} \) \(\mathstrut -\mathstrut 106q^{7} \) \(\mathstrut -\mathstrut 99q^{8} \) \(\mathstrut -\mathstrut 101q^{9} \) \(\mathstrut -\mathstrut 96q^{10} \) \(\mathstrut -\mathstrut 102q^{11} \) \(\mathstrut -\mathstrut 86q^{12} \) \(\mathstrut -\mathstrut 100q^{13} \) \(\mathstrut -\mathstrut 90q^{14} \) \(\mathstrut -\mathstrut 90q^{15} \) \(\mathstrut -\mathstrut 83q^{16} \) \(\mathstrut -\mathstrut 96q^{17} \) \(\mathstrut -\mathstrut 75q^{18} \) \(\mathstrut -\mathstrut 94q^{19} \) \(\mathstrut -\mathstrut 72q^{20} \) \(\mathstrut -\mathstrut 82q^{21} \) \(\mathstrut -\mathstrut 78q^{22} \) \(\mathstrut -\mathstrut 90q^{23} \) \(\mathstrut -\mathstrut 54q^{24} \) \(\mathstrut -\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 72q^{26} \) \(\mathstrut -\mathstrut 74q^{27} \) \(\mathstrut -\mathstrut 58q^{28} \) \(\mathstrut -\mathstrut 84q^{29} \) \(\mathstrut -\mathstrut 42q^{30} \) \(\mathstrut -\mathstrut 82q^{31} \) \(\mathstrut -\mathstrut 51q^{32} \) \(\mathstrut -\mathstrut 66q^{33} \) \(\mathstrut -\mathstrut 60q^{34} \) \(\mathstrut -\mathstrut 66q^{35} \) \(\mathstrut -\mathstrut 23q^{36} \) \(\mathstrut -\mathstrut 76q^{37} \) \(\mathstrut -\mathstrut 54q^{38} \) \(\mathstrut -\mathstrut 58q^{39} \) \(\mathstrut -\mathstrut 24q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 18q^{42} \) \(\mathstrut -\mathstrut 70q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 36q^{45} \) \(\mathstrut -\mathstrut 42q^{46} \) \(\mathstrut -\mathstrut 66q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut 57q^{49} \) \(\mathstrut -\mathstrut 21q^{50} \) \(\mathstrut -\mathstrut 42q^{51} \) \(\mathstrut -\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 60q^{53} \) \(\mathstrut +\mathstrut 6q^{54} \) \(\mathstrut -\mathstrut 42q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 34q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 54q^{59} \) \(\mathstrut +\mathstrut 54q^{60} \) \(\mathstrut -\mathstrut 52q^{61} \) \(\mathstrut -\mathstrut 18q^{62} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut +\mathstrut 13q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut +\mathstrut 30q^{66} \) \(\mathstrut -\mathstrut 46q^{67} \) \(\mathstrut +\mathstrut 12q^{68} \) \(\mathstrut -\mathstrut 18q^{69} \) \(\mathstrut +\mathstrut 30q^{70} \) \(\mathstrut -\mathstrut 42q^{71} \) \(\mathstrut +\mathstrut 81q^{72} \) \(\mathstrut -\mathstrut 40q^{73} \) \(\mathstrut +\mathstrut 10q^{75} \) \(\mathstrut +\mathstrut 26q^{76} \) \(\mathstrut -\mathstrut 18q^{77} \) \(\mathstrut +\mathstrut 54q^{78} \) \(\mathstrut -\mathstrut 34q^{79} \) \(\mathstrut +\mathstrut 72q^{80} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut +\mathstrut 12q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut +\mathstrut 110q^{84} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut +\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 66q^{88} \) \(\mathstrut -\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 120q^{90} \) \(\mathstrut -\mathstrut 2q^{91} \) \(\mathstrut +\mathstrut 54q^{92} \) \(\mathstrut +\mathstrut 14q^{93} \) \(\mathstrut +\mathstrut 30q^{94} \) \(\mathstrut +\mathstrut 6q^{95} \) \(\mathstrut +\mathstrut 138q^{96} \) \(\mathstrut -\mathstrut 16q^{97} \) \(\mathstrut +\mathstrut 57q^{98} \) \(\mathstrut +\mathstrut 42q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(229))\)

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
229.2.a \(\chi_{229}(1, \cdot)\) 229.2.a.a 1 1
229.2.a.b 6
229.2.a.c 11
229.2.b \(\chi_{229}(228, \cdot)\) 229.2.b.a 2 1
229.2.b.b 16
229.2.c \(\chi_{229}(94, \cdot)\) 229.2.c.a 36 2
229.2.e \(\chi_{229}(95, \cdot)\) 229.2.e.a 2 2
229.2.e.b 36
229.2.g \(\chi_{229}(16, \cdot)\) 229.2.g.a 306 18
229.2.h \(\chi_{229}(4, \cdot)\) 229.2.h.a 324 18
229.2.i \(\chi_{229}(3, \cdot)\) 229.2.i.a 648 36
229.2.k \(\chi_{229}(5, \cdot)\) 229.2.k.a 684 36