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Properties

Label 297.2
Level 297
Weight 2
Dimension 2374
Nonzero newspaces 12
Newform subspaces 33
Sturm bound 12960
Trace bound 7

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Defining parameters

Level: \( N \) = \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 33 \)
Sturm bound: \(12960\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(297))\).

Total New Old
Modular forms 3540 2662 878
Cusp forms 2941 2374 567
Eisenstein series 599 288 311

Trace form

\( 2374 q - 28 q^{2} - 48 q^{3} - 54 q^{4} - 34 q^{5} - 60 q^{6} - 56 q^{7} - 52 q^{8} - 60 q^{9} + O(q^{10}) \) \( 2374 q - 28 q^{2} - 48 q^{3} - 54 q^{4} - 34 q^{5} - 60 q^{6} - 56 q^{7} - 52 q^{8} - 60 q^{9} - 64 q^{10} - 43 q^{11} - 144 q^{12} - 68 q^{13} - 70 q^{14} - 78 q^{15} - 78 q^{16} - 58 q^{17} - 78 q^{18} - 50 q^{19} - 54 q^{20} - 36 q^{21} - 73 q^{22} - 66 q^{23} - 24 q^{24} - 86 q^{25} - 20 q^{26} - 42 q^{27} - 200 q^{28} - 58 q^{29} - 42 q^{30} - 88 q^{31} - 120 q^{32} - 60 q^{33} - 198 q^{34} - 114 q^{35} - 96 q^{36} - 106 q^{37} - 184 q^{38} - 126 q^{39} - 172 q^{40} - 100 q^{41} - 96 q^{42} - 112 q^{43} - 73 q^{44} - 102 q^{45} - 64 q^{46} - 10 q^{47} - 30 q^{48} - 82 q^{49} - 24 q^{50} - 24 q^{51} - 108 q^{52} - 44 q^{53} + 48 q^{54} - 188 q^{55} - 114 q^{56} - 54 q^{57} - 192 q^{58} - 86 q^{59} - 60 q^{60} - 132 q^{61} - 166 q^{62} - 78 q^{63} - 158 q^{64} - 136 q^{65} - 51 q^{66} - 200 q^{67} - 208 q^{68} - 78 q^{69} - 160 q^{70} - 174 q^{71} - 96 q^{72} - 108 q^{73} - 246 q^{74} - 138 q^{75} - 82 q^{76} - 135 q^{77} - 156 q^{78} - 60 q^{79} + 196 q^{80} - 72 q^{81} - 116 q^{82} + 22 q^{83} + 168 q^{84} + 144 q^{85} + 188 q^{86} + 72 q^{87} + 280 q^{88} + 152 q^{89} + 204 q^{90} + 48 q^{91} + 598 q^{92} + 168 q^{93} + 280 q^{94} + 426 q^{95} + 420 q^{96} + 122 q^{97} + 550 q^{98} + 207 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)

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
297.2.a \(\chi_{297}(1, \cdot)\) 297.2.a.a 1 1
297.2.a.b 1
297.2.a.c 1
297.2.a.d 1
297.2.a.e 2
297.2.a.f 2
297.2.a.g 3
297.2.a.h 3
297.2.d \(\chi_{297}(296, \cdot)\) 297.2.d.a 8 1
297.2.d.b 8
297.2.e \(\chi_{297}(100, \cdot)\) 297.2.e.a 2 2
297.2.e.b 2
297.2.e.c 2
297.2.e.d 6
297.2.e.e 8
297.2.f \(\chi_{297}(82, \cdot)\) 297.2.f.a 16 4
297.2.f.b 16
297.2.f.c 16
297.2.f.d 16
297.2.g \(\chi_{297}(98, \cdot)\) 297.2.g.a 4 2
297.2.g.b 16
297.2.j \(\chi_{297}(34, \cdot)\) 297.2.j.a 6 6
297.2.j.b 72
297.2.j.c 102
297.2.k \(\chi_{297}(107, \cdot)\) 297.2.k.a 32 4
297.2.k.b 32
297.2.n \(\chi_{297}(37, \cdot)\) 297.2.n.a 8 8
297.2.n.b 72
297.2.o \(\chi_{297}(32, \cdot)\) 297.2.o.a 12 6
297.2.o.b 192
297.2.t \(\chi_{297}(8, \cdot)\) 297.2.t.a 80 8
297.2.u \(\chi_{297}(4, \cdot)\) 297.2.u.a 816 24
297.2.x \(\chi_{297}(2, \cdot)\) 297.2.x.a 816 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(297))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(297)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 2}\)