Properties

Label 294.6
Level 294
Weight 6
Dimension 2821
Nonzero newspaces 8
Sturm bound 28224
Trace bound 4

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Defining parameters

Level: \( N \) = \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(28224\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(294))\).

Total New Old
Modular forms 12000 2821 9179
Cusp forms 11520 2821 8699
Eisenstein series 480 0 480

Trace form

\( 2821q + 4q^{2} + 27q^{3} - 112q^{4} + 198q^{5} + 396q^{6} + 464q^{7} + 64q^{8} - 1383q^{9} + O(q^{10}) \) \( 2821q + 4q^{2} + 27q^{3} - 112q^{4} + 198q^{5} + 396q^{6} + 464q^{7} + 64q^{8} - 1383q^{9} - 3240q^{10} - 1836q^{11} + 432q^{12} + 8670q^{13} + 8658q^{15} + 256q^{16} - 6918q^{17} - 2652q^{18} - 2052q^{19} - 1056q^{20} - 4854q^{21} - 240q^{22} - 7056q^{23} + 3264q^{24} + 36079q^{25} - 7912q^{26} + 2187q^{27} - 11328q^{28} - 28458q^{29} - 30648q^{30} - 2424q^{31} + 1024q^{32} + 73476q^{33} + 53832q^{34} + 23568q^{35} - 29424q^{36} - 180154q^{37} - 4768q^{38} + 39984q^{39} + 114816q^{40} + 159234q^{41} + 66600q^{42} - 42500q^{43} - 36096q^{44} - 70398q^{45} - 210480q^{46} - 101376q^{47} - 25344q^{48} - 742008q^{49} - 133028q^{50} - 9954q^{51} + 49696q^{52} + 86190q^{53} + 117900q^{54} + 1211532q^{55} + 253440q^{56} + 170400q^{57} + 446424q^{58} + 219228q^{59} - 47232q^{60} - 562574q^{61} - 223312q^{62} - 302262q^{63} + 167936q^{64} - 325668q^{65} - 328464q^{66} + 78860q^{67} - 110688q^{68} + 223128q^{69} + 110880q^{70} + 240696q^{71} + 52800q^{72} + 1096386q^{73} + 527480q^{74} + 1007109q^{75} + 149952q^{76} - 129924q^{77} - 174648q^{78} - 1598824q^{79} + 50688q^{80} - 573627q^{81} - 436056q^{82} - 173724q^{83} - 69792q^{84} + 570036q^{85} - 382672q^{86} + 433578q^{87} - 232704q^{88} + 895890q^{89} + 173016q^{90} + 361928q^{91} + 363648q^{92} + 1166076q^{93} + 1009536q^{94} - 841872q^{95} + 52224q^{96} - 1389342q^{97} - 122784q^{98} - 107844q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(294))\)

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
294.6.a \(\chi_{294}(1, \cdot)\) 294.6.a.a 1 1
294.6.a.b 1
294.6.a.c 1
294.6.a.d 1
294.6.a.e 1
294.6.a.f 1
294.6.a.g 1
294.6.a.h 1
294.6.a.i 1
294.6.a.j 1
294.6.a.k 1
294.6.a.l 1
294.6.a.m 1
294.6.a.n 2
294.6.a.o 2
294.6.a.p 2
294.6.a.q 2
294.6.a.r 2
294.6.a.s 2
294.6.a.t 2
294.6.a.u 2
294.6.a.v 2
294.6.a.w 2
294.6.d \(\chi_{294}(293, \cdot)\) 294.6.d.a 28 1
294.6.d.b 40
294.6.e \(\chi_{294}(67, \cdot)\) 294.6.e.a 2 2
294.6.e.b 2
294.6.e.c 2
294.6.e.d 2
294.6.e.e 2
294.6.e.f 2
294.6.e.g 2
294.6.e.h 2
294.6.e.i 2
294.6.e.j 2
294.6.e.k 2
294.6.e.l 2
294.6.e.m 2
294.6.e.n 2
294.6.e.o 2
294.6.e.p 2
294.6.e.q 2
294.6.e.r 2
294.6.e.s 4
294.6.e.t 4
294.6.e.u 4
294.6.e.v 4
294.6.e.w 4
294.6.e.x 4
294.6.e.y 4
294.6.e.z 4
294.6.f \(\chi_{294}(215, \cdot)\) n/a 132 2
294.6.i \(\chi_{294}(43, \cdot)\) n/a 288 6
294.6.j \(\chi_{294}(41, \cdot)\) n/a 552 6
294.6.m \(\chi_{294}(25, \cdot)\) n/a 552 12
294.6.p \(\chi_{294}(5, \cdot)\) n/a 1128 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(294))\) into lower level spaces

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