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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

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

Display 100 coefficients 10 coefficients

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 available 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

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