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Properties

Label 1323.2.bn
Level $1323$
Weight $2$
Character orbit 1323.bn
Rep. character $\chi_{1323}(109,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $900$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.bn (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 2088 900 1188
Cusp forms 1944 900 1044
Eisenstein series 144 0 144

Trace form

\( 900 q + 76 q^{4} - 9 q^{7} + O(q^{10}) \) \( 900 q + 76 q^{4} - 9 q^{7} + 2 q^{10} + 78 q^{16} + 9 q^{19} - 2 q^{22} + 83 q^{25} + 62 q^{28} - 13 q^{31} + 56 q^{34} + 77 q^{37} - 28 q^{40} + 62 q^{43} + 10 q^{46} - 45 q^{49} - 188 q^{52} + 80 q^{55} - 172 q^{58} - 43 q^{61} - 200 q^{64} + 2 q^{67} - 68 q^{70} - 7 q^{73} - 260 q^{76} - 10 q^{79} + 188 q^{82} + 60 q^{85} + 30 q^{88} - 88 q^{91} - 170 q^{94} + 14 q^{97} + O(q^{100}) \)

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

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