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Properties

Label 798.4.bn
Level $798$
Weight $4$
Character orbit 798.bn
Rep. character $\chi_{798}(353,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
Sturm bound $640$

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Defining parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 798.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 399 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(798, [\chi])\).

Total New Old
Modular forms 976 320 656
Cusp forms 944 320 624
Eisenstein series 32 0 32

Trace form

\( 320 q - 1280 q^{4} - 74 q^{7} + O(q^{10}) \) \( 320 q - 1280 q^{4} - 74 q^{7} - 186 q^{13} - 40 q^{15} + 5120 q^{16} + 16 q^{18} - 342 q^{19} - 48 q^{21} - 72 q^{22} + 7928 q^{25} + 296 q^{28} - 136 q^{30} - 390 q^{31} - 360 q^{34} + 710 q^{37} - 454 q^{39} + 1372 q^{42} - 322 q^{43} - 2040 q^{45} - 432 q^{46} - 1318 q^{49} + 800 q^{51} + 744 q^{52} - 516 q^{57} + 168 q^{58} + 160 q^{60} - 4512 q^{61} - 1580 q^{63} - 20480 q^{64} - 2156 q^{67} + 1056 q^{70} - 64 q^{72} - 5418 q^{73} - 3354 q^{75} + 1368 q^{76} + 712 q^{78} - 308 q^{79} - 1064 q^{81} + 192 q^{84} - 468 q^{85} - 2616 q^{87} + 288 q^{88} + 6192 q^{90} + 4152 q^{91} + 2360 q^{93} + 7344 q^{94} + 13044 q^{97} - 6492 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(798, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(798, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(798, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)