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Properties

Label 294.6.i
Level $294$
Weight $6$
Character orbit 294.i
Rep. character $\chi_{294}(43,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $288$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 294.i (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(294, [\chi])\).

Total New Old
Modular forms 1704 288 1416
Cusp forms 1656 288 1368
Eisenstein series 48 0 48

Trace form

\( 288 q + 18 q^{3} - 768 q^{4} + 88 q^{5} + 72 q^{6} - 176 q^{7} - 3888 q^{9} + O(q^{10}) \) \( 288 q + 18 q^{3} - 768 q^{4} + 88 q^{5} + 72 q^{6} - 176 q^{7} - 3888 q^{9} - 96 q^{10} + 1620 q^{11} + 288 q^{12} + 1352 q^{13} - 704 q^{14} + 990 q^{15} - 12288 q^{16} - 5988 q^{17} - 7940 q^{19} - 3520 q^{20} + 702 q^{21} - 8328 q^{22} - 2552 q^{23} + 1152 q^{24} - 24748 q^{25} + 4400 q^{26} + 1458 q^{27} - 2816 q^{28} + 7032 q^{29} + 4208 q^{31} - 360 q^{33} + 15360 q^{34} + 3468 q^{35} - 62208 q^{36} - 29254 q^{37} - 2864 q^{38} + 1710 q^{39} + 26240 q^{40} + 68984 q^{41} + 44136 q^{42} - 8828 q^{43} - 11712 q^{44} - 17820 q^{45} + 23840 q^{46} + 110708 q^{47} - 27648 q^{48} - 138048 q^{49} - 48064 q^{50} - 52200 q^{51} - 16224 q^{52} + 39152 q^{53} + 5832 q^{54} + 284922 q^{55} + 87296 q^{56} - 19332 q^{57} + 72360 q^{58} - 124460 q^{59} + 15840 q^{60} + 27622 q^{61} - 41296 q^{62} - 69822 q^{63} - 196608 q^{64} - 123032 q^{65} + 34848 q^{66} - 48052 q^{67} - 10240 q^{68} - 83520 q^{69} - 215224 q^{70} + 77576 q^{71} - 158044 q^{73} - 209936 q^{74} + 59886 q^{75} + 34688 q^{76} - 7052 q^{77} + 41760 q^{78} - 49424 q^{79} + 22528 q^{80} - 314928 q^{81} - 62976 q^{82} + 156748 q^{83} + 11232 q^{84} + 311120 q^{85} + 560624 q^{86} - 152586 q^{87} + 213504 q^{88} + 427244 q^{89} - 7776 q^{90} - 77756 q^{91} - 40832 q^{92} + 106092 q^{93} + 79504 q^{94} - 259592 q^{95} + 18432 q^{96} + 1118880 q^{97} + 29760 q^{98} - 47952 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(294, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(294, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(294, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)