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Properties

Label 1521.2.bn
Level $1521$
Weight $2$
Character orbit 1521.bn
Rep. character $\chi_{1521}(8,\cdot)$
Character field $\Q(\zeta_{52})$
Dimension $1488$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1521.bn (of order \(52\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 507 \)
Character field: \(\Q(\zeta_{52})\)
Sturm bound: \(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1521, [\chi])\).

Total New Old
Modular forms 4464 1488 2976
Cusp forms 4272 1488 2784
Eisenstein series 192 0 192

Trace form

\( 1488 q + 8 q^{7} + O(q^{10}) \) \( 1488 q + 8 q^{7} + 4 q^{13} + 148 q^{16} + 8 q^{19} + 12 q^{34} - 12 q^{37} - 80 q^{40} + 72 q^{46} - 40 q^{52} - 352 q^{55} + 92 q^{58} + 24 q^{61} + 352 q^{67} + 328 q^{70} - 4 q^{73} - 48 q^{76} + 32 q^{79} - 520 q^{82} - 24 q^{85} - 64 q^{91} + 296 q^{94} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1521, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1521, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1521, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 2}\)