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Properties

Label 294.4.j
Level $294$
Weight $4$
Character orbit 294.j
Rep. character $\chi_{294}(41,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $336$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.j (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(294, [\chi])\).

Total New Old
Modular forms 1032 336 696
Cusp forms 984 336 648
Eisenstein series 48 0 48

Trace form

\( 336 q + 224 q^{4} + 28 q^{6} - 4 q^{7} - 70 q^{9} + O(q^{10}) \) \( 336 q + 224 q^{4} + 28 q^{6} - 4 q^{7} - 70 q^{9} - 168 q^{15} - 896 q^{16} + 112 q^{18} + 168 q^{21} - 420 q^{22} - 1484 q^{25} - 84 q^{27} + 16 q^{28} - 448 q^{30} + 280 q^{36} - 1162 q^{37} + 140 q^{39} - 336 q^{40} + 1252 q^{42} + 1540 q^{43} + 1904 q^{45} + 2520 q^{46} + 496 q^{49} - 1428 q^{51} - 2072 q^{52} - 4326 q^{55} + 2128 q^{57} - 3780 q^{58} + 672 q^{60} + 2842 q^{61} + 2496 q^{63} + 3584 q^{64} - 364 q^{67} - 1820 q^{69} - 2412 q^{70} - 448 q^{72} - 4620 q^{75} + 224 q^{78} - 952 q^{79} - 6062 q^{81} - 1344 q^{84} + 5544 q^{85} - 728 q^{87} - 672 q^{88} - 6972 q^{90} - 9480 q^{91} + 8876 q^{93} - 8736 q^{94} + 17836 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(294, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(294, [\chi])\) into lower level spaces

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