Properties

Label 784.4.w
Level $784$
Weight $4$
Character orbit 784.w
Rep. character $\chi_{784}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $944$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 784.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(784, [\chi])\).

Total New Old
Modular forms 1376 976 400
Cusp forms 1312 944 368
Eisenstein series 64 32 32

Trace form

\( 944q + 2q^{2} + 6q^{3} + 22q^{4} + 6q^{5} + 68q^{8} + O(q^{10}) \) \( 944q + 2q^{2} + 6q^{3} + 22q^{4} + 6q^{5} + 68q^{8} - 12q^{10} - 38q^{11} + 6q^{12} + 302q^{16} + 12q^{17} - 172q^{18} + 6q^{19} - 992q^{22} + 660q^{23} + 6q^{24} + 6q^{26} - 816q^{29} - 1174q^{30} + 492q^{32} + 12q^{33} + 1120q^{36} + 18q^{37} + 6q^{38} + 4q^{39} - 2334q^{40} - 1632q^{43} + 656q^{44} - 156q^{45} - 284q^{46} + 2844q^{50} - 914q^{51} - 156q^{52} - 750q^{53} + 5754q^{54} + 1900q^{58} + 2070q^{59} + 862q^{60} + 6q^{61} - 5924q^{64} + 4q^{65} + 810q^{66} + 2966q^{67} - 3024q^{68} - 480q^{71} - 8058q^{72} + 3404q^{74} - 744q^{75} + 9620q^{78} - 3756q^{80} + 33052q^{81} - 5166q^{82} + 484q^{85} + 2766q^{86} + 12q^{87} - 3864q^{88} + 6076q^{92} + 218q^{93} + 7026q^{94} + 17436q^{96} - 592q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(784, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(784, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(784, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)