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Properties

Label 1380.2.h
Level $1380$
Weight $2$
Character orbit 1380.h
Rep. character $\chi_{1380}(1151,\cdot)$
Character field $\Q$
Dimension $176$
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.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Sturm bound: \(576\)

Dimensions

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

Total New Old
Modular forms 296 176 120
Cusp forms 280 176 104
Eisenstein series 16 0 16

Trace form

\( 176 q + 6 q^{6} + 8 q^{9} + O(q^{10}) \) \( 176 q + 6 q^{6} + 8 q^{9} - 14 q^{12} + 16 q^{13} - 26 q^{18} - 24 q^{22} + 4 q^{24} - 176 q^{25} - 24 q^{28} - 16 q^{30} + 32 q^{33} + 24 q^{34} + 10 q^{36} - 16 q^{37} + 64 q^{42} + 38 q^{48} - 224 q^{49} + 60 q^{52} + 20 q^{54} - 48 q^{57} + 36 q^{58} + 28 q^{60} - 16 q^{61} + 12 q^{64} - 12 q^{66} + 24 q^{70} - 44 q^{72} + 16 q^{76} - 6 q^{78} - 40 q^{81} + 4 q^{82} - 88 q^{84} - 40 q^{88} - 36 q^{90} - 48 q^{93} - 36 q^{94} + 30 q^{96} + 96 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1380, [\chi]) \cong \)