Properties

Label 294.2
Level 294
Weight 2
Dimension 563
Nonzero newspaces 8
Newform subspaces 28
Sturm bound 9408
Trace bound 4

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Defining parameters

Level: \( N \) = \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 28 \)
Sturm bound: \(9408\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(294))\).

Total New Old
Modular forms 2592 563 2029
Cusp forms 2113 563 1550
Eisenstein series 479 0 479

Trace form

\( 563q - q^{2} + 3q^{3} + 7q^{4} + 18q^{5} + 11q^{6} + 16q^{7} - q^{8} + 15q^{9} + O(q^{10}) \) \( 563q - q^{2} + 3q^{3} + 7q^{4} + 18q^{5} + 11q^{6} + 16q^{7} - q^{8} + 15q^{9} + 18q^{10} + 36q^{11} + 3q^{12} + 18q^{13} - 6q^{15} - q^{16} + 6q^{17} - 25q^{18} + 12q^{19} - 6q^{20} - 10q^{21} - 12q^{22} - 13q^{24} + 17q^{25} + 10q^{26} + 3q^{27} + 12q^{28} + 18q^{29} + 18q^{30} + 48q^{31} - q^{32} + 36q^{33} + 30q^{34} + 48q^{35} + 15q^{36} - 38q^{37} - 32q^{38} - 56q^{39} - 66q^{40} - 114q^{41} - 54q^{42} - 52q^{43} - 48q^{44} - 66q^{45} - 180q^{46} - 144q^{47} - 11q^{48} - 288q^{49} - 103q^{50} - 210q^{51} - 58q^{52} - 150q^{53} - 37q^{54} - 420q^{55} - 72q^{56} - 48q^{57} - 222q^{58} - 132q^{59} - 72q^{60} - 178q^{61} - 68q^{62} - 30q^{63} + 7q^{64} + 84q^{65} - 12q^{66} - 20q^{67} + 6q^{68} + 24q^{69} + 72q^{71} + 23q^{72} + 30q^{73} + 34q^{74} + 45q^{75} + 12q^{76} + 108q^{77} + 34q^{78} + 160q^{79} + 18q^{80} + 27q^{81} + 102q^{82} - 12q^{83} + 26q^{84} + 108q^{85} + 76q^{86} - 78q^{87} + 12q^{88} - 66q^{89} + 18q^{90} - 56q^{91} + 24q^{92} - 228q^{93} + 96q^{94} - 240q^{95} - 13q^{96} - 66q^{97} + 24q^{98} - 180q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)

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
294.2.a \(\chi_{294}(1, \cdot)\) 294.2.a.a 1 1
294.2.a.b 1
294.2.a.c 1
294.2.a.d 1
294.2.a.e 1
294.2.a.f 1
294.2.a.g 1
294.2.d \(\chi_{294}(293, \cdot)\) 294.2.d.a 4 1
294.2.d.b 8
294.2.e \(\chi_{294}(67, \cdot)\) 294.2.e.a 2 2
294.2.e.b 2
294.2.e.c 2
294.2.e.d 2
294.2.e.e 2
294.2.e.f 2
294.2.f \(\chi_{294}(215, \cdot)\) 294.2.f.a 4 2
294.2.f.b 8
294.2.f.c 16
294.2.i \(\chi_{294}(43, \cdot)\) 294.2.i.a 6 6
294.2.i.b 12
294.2.i.c 12
294.2.i.d 18
294.2.j \(\chi_{294}(41, \cdot)\) 294.2.j.a 120 6
294.2.m \(\chi_{294}(25, \cdot)\) 294.2.m.a 24 12
294.2.m.b 24
294.2.m.c 36
294.2.m.d 36
294.2.p \(\chi_{294}(5, \cdot)\) 294.2.p.a 216 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(294))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(294)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)