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Properties

Label 245.6.p
Level $245$
Weight $6$
Character orbit 245.p
Rep. character $\chi_{245}(29,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $828$
Sturm bound $168$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 245.p (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(168\)

Dimensions

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

Total New Old
Modular forms 852 852 0
Cusp forms 828 828 0
Eisenstein series 24 24 0

Trace form

\( 828 q + 2166 q^{4} + 17 q^{5} - 82 q^{6} + 9894 q^{9} + O(q^{10}) \) \( 828 q + 2166 q^{4} + 17 q^{5} - 82 q^{6} + 9894 q^{9} - 31 q^{10} - 780 q^{11} - 1590 q^{14} + 1585 q^{15} - 34690 q^{16} - 18212 q^{19} + 6333 q^{20} + 4616 q^{21} + 13738 q^{24} - 1875 q^{25} - 12010 q^{26} - 32880 q^{29} - 456 q^{30} + 47140 q^{31} + 59730 q^{34} - 7005 q^{35} - 116854 q^{36} - 44462 q^{39} - 126419 q^{40} + 35052 q^{41} - 1766 q^{44} - 29545 q^{45} - 7258 q^{46} + 36640 q^{49} - 289882 q^{50} + 37694 q^{51} - 84008 q^{54} + 128091 q^{55} + 201958 q^{56} + 40650 q^{59} - 194385 q^{60} - 193946 q^{61} + 495594 q^{64} - 54011 q^{65} + 404376 q^{66} + 24182 q^{69} + 168507 q^{70} + 402440 q^{71} + 332366 q^{74} - 131533 q^{75} - 12308 q^{76} - 262912 q^{79} + 469432 q^{80} - 1321666 q^{81} + 1223634 q^{84} - 62653 q^{85} - 72838 q^{86} + 288304 q^{89} - 571208 q^{90} - 407690 q^{91} + 422310 q^{94} + 543256 q^{95} - 380092 q^{96} + 1011600 q^{99} + O(q^{100}) \)

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.