Properties

Label 294.4
Level 294
Weight 4
Dimension 1693
Nonzero newspaces 8
Sturm bound 18816
Trace bound 3

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Defining parameters

Level: \( N \) = \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(18816\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(294))\).

Total New Old
Modular forms 7296 1693 5603
Cusp forms 6816 1693 5123
Eisenstein series 480 0 480

Trace form

\( 1693q - 2q^{2} + 21q^{3} + 4q^{4} - 90q^{5} - 66q^{6} - 96q^{7} - 8q^{8} + 93q^{9} + O(q^{10}) \) \( 1693q - 2q^{2} + 21q^{3} + 4q^{4} - 90q^{5} - 66q^{6} - 96q^{7} - 8q^{8} + 93q^{9} + 132q^{10} + 180q^{11} + 84q^{12} + 14q^{13} - 522q^{15} + 16q^{16} - 150q^{17} + 318q^{18} + 788q^{19} + 24q^{20} + 648q^{21} - 24q^{22} + 120q^{24} + 751q^{25} + 836q^{26} - 135q^{27} + 96q^{28} - 162q^{29} - 1308q^{30} - 1624q^{31} - 32q^{32} - 2664q^{33} - 1380q^{34} - 876q^{35} - 1596q^{36} - 7978q^{37} - 4816q^{38} - 2214q^{39} - 1488q^{40} - 534q^{41} + 828q^{42} + 2780q^{43} + 3072q^{44} + 7002q^{45} + 9576q^{46} + 8352q^{47} + 432q^{48} + 12228q^{49} + 3490q^{50} + 1134q^{51} - 280q^{52} + 2382q^{53} - 306q^{54} + 5688q^{55} - 576q^{56} + 1620q^{57} - 2076q^{58} - 6132q^{59} - 576q^{60} - 6346q^{61} - 4648q^{62} + 2406q^{63} + 1600q^{64} + 1572q^{65} + 4104q^{66} - 460q^{67} - 600q^{68} - 3816q^{69} - 1008q^{70} - 6840q^{71} - 1416q^{72} - 11590q^{73} + 500q^{74} - 9753q^{75} - 784q^{76} + 108q^{77} - 6012q^{78} - 4552q^{79} - 1440q^{80} - 14871q^{81} - 4020q^{82} - 13524q^{83} - 912q^{84} - 5820q^{85} - 2248q^{86} - 7098q^{87} + 1248q^{88} - 798q^{89} - 2268q^{90} + 8064q^{91} - 3552q^{92} + 15216q^{93} - 3648q^{94} + 21624q^{95} + 480q^{96} + 6674q^{97} - 816q^{98} + 16572q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(294))\)

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
294.4.a \(\chi_{294}(1, \cdot)\) 294.4.a.a 1 1
294.4.a.b 1
294.4.a.c 1
294.4.a.d 1
294.4.a.e 1
294.4.a.f 1
294.4.a.g 1
294.4.a.h 1
294.4.a.i 1
294.4.a.j 2
294.4.a.k 2
294.4.a.l 2
294.4.a.m 2
294.4.a.n 2
294.4.a.o 2
294.4.d \(\chi_{294}(293, \cdot)\) 294.4.d.a 16 1
294.4.d.b 24
294.4.e \(\chi_{294}(67, \cdot)\) 294.4.e.a 2 2
294.4.e.b 2
294.4.e.c 2
294.4.e.d 2
294.4.e.e 2
294.4.e.f 2
294.4.e.g 2
294.4.e.h 2
294.4.e.i 2
294.4.e.j 2
294.4.e.k 4
294.4.e.l 4
294.4.e.m 4
294.4.e.n 4
294.4.e.o 4
294.4.f \(\chi_{294}(215, \cdot)\) 294.4.f.a 16 2
294.4.f.b 16
294.4.f.c 48
294.4.i \(\chi_{294}(43, \cdot)\) n/a 168 6
294.4.j \(\chi_{294}(41, \cdot)\) n/a 336 6
294.4.m \(\chi_{294}(25, \cdot)\) n/a 336 12
294.4.p \(\chi_{294}(5, \cdot)\) n/a 672 12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(294))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(294)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)