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Properties

Label 245.6.j
Level $245$
Weight $6$
Character orbit 245.j
Rep. character $\chi_{245}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
Sturm bound $168$

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Defining parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 245.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(168\)

Dimensions

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

Total New Old
Modular forms 296 208 88
Cusp forms 264 192 72
Eisenstein series 32 16 16

Trace form

\( 192 q + 1474 q^{4} + 12 q^{5} - 72 q^{6} + 7540 q^{9} + O(q^{10}) \) \( 192 q + 1474 q^{4} + 12 q^{5} - 72 q^{6} + 7540 q^{9} + 84 q^{10} + 550 q^{11} - 1188 q^{15} - 21946 q^{16} - 3316 q^{19} + 1096 q^{20} - 3300 q^{24} + 1742 q^{25} + 13570 q^{26} - 23120 q^{29} - 14930 q^{30} + 14860 q^{31} + 38880 q^{34} + 302700 q^{36} + 6670 q^{39} - 17098 q^{40} - 111852 q^{41} + 14118 q^{44} - 30876 q^{45} - 20498 q^{46} - 110116 q^{50} + 63966 q^{51} - 20724 q^{54} + 180520 q^{55} - 89124 q^{59} + 23312 q^{60} + 23122 q^{61} - 402516 q^{64} + 25958 q^{65} + 286316 q^{66} + 110564 q^{69} + 74104 q^{71} - 239078 q^{74} + 68328 q^{75} - 417020 q^{76} - 95670 q^{79} - 263952 q^{80} - 910216 q^{81} - 716336 q^{85} + 539036 q^{86} - 302422 q^{89} + 92524 q^{90} - 305370 q^{94} + 400400 q^{95} + 169668 q^{96} + 188664 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{6}^{\mathrm{old}}(245, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(245, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)