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Properties

Label 1323.4.p
Level $1323$
Weight $4$
Character orbit 1323.p
Rep. character $\chi_{1323}(80,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $320$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1323.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1323, [\chi])\).

Total New Old
Modular forms 1056 320 736
Cusp forms 960 320 640
Eisenstein series 96 0 96

Trace form

\( 320 q + 640 q^{4} + O(q^{10}) \) \( 320 q + 640 q^{4} - 36 q^{10} - 2080 q^{16} - 306 q^{19} + 324 q^{22} - 3946 q^{25} + 24 q^{31} + 50 q^{37} - 1602 q^{40} - 2668 q^{43} + 1518 q^{46} + 498 q^{52} + 2136 q^{58} - 276 q^{61} - 8156 q^{64} + 4372 q^{67} - 558 q^{73} - 1100 q^{79} - 5094 q^{82} - 8640 q^{85} - 6924 q^{88} - 9882 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)