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Properties

Label 1521.2.cd
Level $1521$
Weight $2$
Character orbit 1521.cd
Rep. character $\chi_{1521}(71,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $2880$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1521.cd (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 507 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(364\)

Dimensions

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

Total New Old
Modular forms 8928 2880 6048
Cusp forms 8544 2880 5664
Eisenstein series 384 0 384

Trace form

\( 2880 q - 4 q^{7} + O(q^{10}) \) \( 2880 q - 4 q^{7} + 12 q^{10} + 20 q^{13} - 108 q^{16} - 4 q^{19} - 16 q^{28} - 28 q^{31} - 60 q^{34} - 16 q^{37} + 80 q^{40} - 12 q^{43} + 60 q^{49} + 24 q^{52} + 448 q^{55} + 4 q^{58} + 12 q^{61} - 384 q^{67} - 472 q^{70} - 88 q^{73} - 56 q^{76} - 32 q^{79} + 496 q^{82} - 72 q^{85} + 68 q^{91} - 320 q^{94} + 80 q^{97} + O(q^{100}) \)

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

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