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Properties

Label 1380.2.bu
Level $1380$
Weight $2$
Character orbit 1380.bu
Rep. character $\chi_{1380}(77,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $960$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1380.bu (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 345 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1380, [\chi])\).

Total New Old
Modular forms 6000 960 5040
Cusp forms 5520 960 4560
Eisenstein series 480 0 480

Trace form

\( 960 q - 4 q^{3} + O(q^{10}) \) \( 960 q - 4 q^{3} + 8 q^{13} + 8 q^{15} - 40 q^{25} + 8 q^{27} - 16 q^{31} - 18 q^{33} + 96 q^{37} + 24 q^{43} + 16 q^{51} + 8 q^{55} - 16 q^{57} + 120 q^{61} - 12 q^{63} - 8 q^{67} + 52 q^{75} + 88 q^{81} - 8 q^{85} - 56 q^{87} - 48 q^{91} - 8 q^{93} + 132 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1380, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1380, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)