Properties

Label 1323.2.u
Level $1323$
Weight $2$
Character orbit 1323.u
Rep. character $\chi_{1323}(190,\cdot)$
Character field $\Q(\zeta_{7})$
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.u (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
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

\( 444q - 72q^{4} + q^{7} + O(q^{10}) \) \( 444q - 72q^{4} + q^{7} + 4q^{10} + 2q^{13} - 68q^{16} + 2q^{19} + 2q^{22} - 58q^{25} - 28q^{28} - 12q^{31} - 20q^{34} - 7q^{37} - 50q^{40} - 48q^{43} + 20q^{46} - 23q^{49} + 42q^{52} + 172q^{55} + 76q^{58} - 7q^{61} - 24q^{64} + 18q^{67} - 100q^{70} + 6q^{73} + 268q^{76} - 6q^{79} - 98q^{82} - 60q^{85} + 60q^{88} + 141q^{91} + 152q^{94} + 66q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)