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Properties

Label 294.6.f
Level $294$
Weight $6$
Character orbit 294.f
Rep. character $\chi_{294}(215,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $132$
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.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 592 132 460
Cusp forms 528 132 396
Eisenstein series 64 0 64

Trace form

\( 132 q + 1056 q^{4} + 250 q^{9} + O(q^{10}) \) \( 132 q + 1056 q^{4} + 250 q^{9} - 744 q^{10} + 3204 q^{15} - 16896 q^{16} - 2768 q^{18} - 2652 q^{19} - 5200 q^{22} + 1920 q^{24} - 35516 q^{25} + 608 q^{30} - 22458 q^{31} + 43542 q^{33} + 8000 q^{36} + 23208 q^{37} - 29572 q^{39} - 11904 q^{40} + 71616 q^{43} - 5796 q^{45} + 4176 q^{46} + 45324 q^{51} + 41472 q^{52} + 60408 q^{54} - 30104 q^{57} - 57256 q^{58} + 25632 q^{60} - 298200 q^{61} - 540672 q^{64} - 165312 q^{66} + 67756 q^{67} + 44288 q^{72} + 427596 q^{73} + 458640 q^{75} - 98944 q^{78} - 468886 q^{79} + 444954 q^{81} - 118176 q^{82} + 642936 q^{85} - 833454 q^{87} - 41600 q^{88} + 814800 q^{93} + 444576 q^{94} + 30720 q^{96} - 670768 q^{99} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)