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Properties

Label 245.6.x
Level $245$
Weight $6$
Character orbit 245.x
Rep. character $\chi_{245}(3,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $3312$
Sturm bound $168$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 245.x (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(168\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(245, [\chi])\).

Total New Old
Modular forms 3408 3408 0
Cusp forms 3312 3312 0
Eisenstein series 96 96 0

Trace form

\( 3312 q - 26 q^{2} - 22 q^{3} - 88 q^{5} - 616 q^{6} - 218 q^{7} - 384 q^{8} + O(q^{10}) \) \( 3312 q - 26 q^{2} - 22 q^{3} - 88 q^{5} - 616 q^{6} - 218 q^{7} - 384 q^{8} + 1466 q^{10} - 72 q^{11} - 214 q^{12} - 28 q^{13} + 172 q^{15} - 66876 q^{16} + 4254 q^{17} - 370 q^{18} - 28 q^{20} - 6188 q^{21} - 7268 q^{22} + 2526 q^{23} + 2196 q^{25} + 3476 q^{26} - 28 q^{27} - 35046 q^{28} - 9670 q^{30} + 2388 q^{31} + 60774 q^{32} + 72152 q^{33} + 30620 q^{35} + 580504 q^{36} + 2680 q^{37} - 43788 q^{38} - 140146 q^{40} - 108976 q^{41} - 210274 q^{42} - 58424 q^{43} + 13680 q^{45} + 258348 q^{46} + 236066 q^{47} - 456536 q^{50} + 135668 q^{51} - 68452 q^{52} + 280694 q^{53} - 158746 q^{55} - 541212 q^{56} - 25428 q^{57} - 155882 q^{58} - 106006 q^{60} - 21024 q^{61} - 476 q^{62} - 144664 q^{63} + 44680 q^{65} + 675024 q^{66} + 103832 q^{67} + 394470 q^{68} - 67280 q^{70} - 378800 q^{71} + 704778 q^{72} + 295736 q^{73} - 310906 q^{75} + 28616 q^{76} + 130252 q^{77} - 422284 q^{78} - 594798 q^{80} - 2948796 q^{81} + 739258 q^{82} - 1050378 q^{83} + 193644 q^{85} + 60328 q^{86} - 358114 q^{87} - 1892652 q^{88} - 379372 q^{90} + 1032412 q^{91} + 146072 q^{92} + 210608 q^{93} - 180894 q^{95} - 236996 q^{96} + 1885164 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(245, [\chi])\) into newform subspaces

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