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Properties

Label 1080.2.w
Level $1080$
Weight $2$
Character orbit 1080.w
Rep. character $\chi_{1080}(163,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
Sturm bound $432$

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Defining parameters

Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1080.w (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Sturm bound: \(432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1080, [\chi])\).

Total New Old
Modular forms 456 192 264
Cusp forms 408 192 216
Eisenstein series 48 0 48

Trace form

\( 192 q + O(q^{10}) \) \( 192 q - 8 q^{10} + 4 q^{16} + 8 q^{22} - 16 q^{28} - 28 q^{40} + 32 q^{43} + 36 q^{46} + 12 q^{52} + 40 q^{58} - 76 q^{70} - 52 q^{76} + 124 q^{82} - 40 q^{88} + 16 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1080, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1080, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1080, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 3}\)