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Properties

Label 1323.2.z
Level $1323$
Weight $2$
Character orbit 1323.z
Rep. character $\chi_{1323}(188,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $444$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.z (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1323, [\chi])\).

Total New Old
Modular forms 1044 444 600
Cusp forms 972 444 528
Eisenstein series 72 0 72

Trace form

\( 444 q + 72 q^{4} + 3 q^{7} + O(q^{10}) \) \( 444 q + 72 q^{4} + 3 q^{7} - 68 q^{16} + 22 q^{22} - 82 q^{25} + 16 q^{28} - 56 q^{34} + 23 q^{37} - 14 q^{40} - 16 q^{43} + 20 q^{46} + 57 q^{49} - 14 q^{52} + 84 q^{58} + 21 q^{61} + 72 q^{64} - 14 q^{67} - 20 q^{70} - 336 q^{76} + 42 q^{79} - 70 q^{82} + 84 q^{85} + 12 q^{88} + 281 q^{91} + 308 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

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