Properties

Label 294.4.p
Level $294$
Weight $4$
Character orbit 294.p
Rep. character $\chi_{294}(5,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $672$
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.p (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 2064 672 1392
Cusp forms 1968 672 1296
Eisenstein series 96 0 96

Trace form

\( 672 q - 224 q^{4} - 28 q^{6} - 80 q^{7} + 112 q^{9} + O(q^{10}) \) \( 672 q - 224 q^{4} - 28 q^{6} - 80 q^{7} + 112 q^{9} + 36 q^{10} + 168 q^{15} + 896 q^{16} + 56 q^{18} + 342 q^{19} + 450 q^{21} + 420 q^{22} + 48 q^{24} + 1358 q^{25} + 84 q^{27} - 88 q^{28} - 224 q^{30} - 804 q^{31} - 1332 q^{33} - 280 q^{36} - 5516 q^{37} + 70 q^{39} - 528 q^{40} - 856 q^{42} - 2044 q^{43} + 490 q^{45} + 6552 q^{46} + 4556 q^{49} - 714 q^{51} + 1832 q^{52} - 180 q^{54} + 6342 q^{55} - 2128 q^{57} + 2520 q^{58} + 336 q^{60} - 8806 q^{61} + 2016 q^{63} + 7168 q^{64} + 2016 q^{66} + 574 q^{67} + 1820 q^{69} + 2664 q^{70} - 224 q^{72} - 3294 q^{73} - 1554 q^{75} - 224 q^{78} + 784 q^{79} - 8764 q^{81} - 432 q^{82} + 1104 q^{84} - 5544 q^{85} - 2482 q^{87} - 336 q^{88} + 6972 q^{90} + 5646 q^{91} + 10024 q^{93} + 4848 q^{94} + 192 q^{96} - 17836 q^{99} + O(q^{100}) \)

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

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