Properties

Label 784.4.j
Level $784$
Weight $4$
Character orbit 784.j
Rep. character $\chi_{784}(195,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $472$
Sturm bound $448$

Related objects

Downloads

Learn more about

Defining parameters

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

Dimensions

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

Total New Old
Modular forms 688 488 200
Cusp forms 656 472 184
Eisenstein series 32 16 16

Trace form

\( 472q + 4q^{2} - 16q^{4} - 92q^{8} + O(q^{10}) \) \( 472q + 4q^{2} - 16q^{4} - 92q^{8} + 44q^{11} - 296q^{16} + 388q^{18} + 260q^{22} - 648q^{23} - 408q^{29} + 1132q^{30} + 984q^{32} + 176q^{36} - 12q^{37} + 8q^{39} - 816q^{43} - 188q^{44} - 760q^{46} - 768q^{50} - 1180q^{51} + 756q^{53} - 2860q^{58} + 1700q^{60} + 4472q^{64} + 8q^{65} - 188q^{67} + 432q^{71} + 4992q^{72} - 164q^{74} - 9212q^{78} - 33040q^{81} - 508q^{85} + 2112q^{86} + 4332q^{88} + 7580q^{92} - 212q^{93} - 4832q^{99} + O(q^{100}) \)

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

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