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Properties

Label 242.2
Level 242
Weight 2
Dimension 596
Nonzero newspaces 4
Newform subspaces 17
Sturm bound 7260
Trace bound 1

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Defining parameters

Level: \( N \) = \( 242 = 2 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 17 \)
Sturm bound: \(7260\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(242))\).

Total New Old
Modular forms 1975 596 1379
Cusp forms 1656 596 1060
Eisenstein series 319 0 319

Trace form

\( 596 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + q^{8} - 27 q^{9} + O(q^{10}) \) \( 596 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + q^{8} - 27 q^{9} - 14 q^{10} - 10 q^{11} - 16 q^{12} - 6 q^{13} - 12 q^{14} - 36 q^{15} + q^{16} - 22 q^{17} + 3 q^{18} - 10 q^{19} + 6 q^{20} - 8 q^{21} - 16 q^{23} - 6 q^{24} - 49 q^{25} - 26 q^{26} - 50 q^{27} - 12 q^{28} - 50 q^{29} - 36 q^{30} - 28 q^{31} - 9 q^{32} - 55 q^{33} - 22 q^{34} - 72 q^{35} + 3 q^{36} - 2 q^{37} - 40 q^{38} - 44 q^{39} - 14 q^{40} - 38 q^{41} - 28 q^{42} - 56 q^{43} - 15 q^{44} - 22 q^{45} - 16 q^{46} - 32 q^{47} + 4 q^{48} - 63 q^{49} - 9 q^{50} - 58 q^{51} - 26 q^{52} - 46 q^{53} - 40 q^{54} - 70 q^{55} + 8 q^{56} - 90 q^{57} - 50 q^{58} - 70 q^{59} - 16 q^{60} - 78 q^{61} - 28 q^{62} - 136 q^{63} + q^{64} - 116 q^{65} - 60 q^{66} - 112 q^{67} - 22 q^{68} - 124 q^{69} - 32 q^{70} - 88 q^{71} - 27 q^{72} - 46 q^{73} - 2 q^{74} - 106 q^{75} - 80 q^{77} - 24 q^{78} - 20 q^{79} - 14 q^{80} - 149 q^{81} - 28 q^{82} - 46 q^{83} - 48 q^{84} - 112 q^{85} - 86 q^{86} - 80 q^{87} - 10 q^{88} - 70 q^{89} - 102 q^{90} - 88 q^{91} - 36 q^{92} - 132 q^{93} - 72 q^{94} - 100 q^{95} + 4 q^{96} - 92 q^{97} - 33 q^{98} - 130 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)

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
242.2.a \(\chi_{242}(1, \cdot)\) 242.2.a.a 1 1
242.2.a.b 1
242.2.a.c 2
242.2.a.d 2
242.2.a.e 2
242.2.a.f 2
242.2.c \(\chi_{242}(3, \cdot)\) 242.2.c.a 4 4
242.2.c.b 4
242.2.c.c 4
242.2.c.d 4
242.2.c.e 4
242.2.c.f 8
242.2.c.g 8
242.2.e \(\chi_{242}(23, \cdot)\) 242.2.e.a 50 10
242.2.e.b 60
242.2.g \(\chi_{242}(5, \cdot)\) 242.2.g.a 200 40
242.2.g.b 240

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(242))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(242)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)