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Properties

Label 1064.2.i
Level $1064$
Weight $2$
Character orbit 1064.i
Rep. character $\chi_{1064}(419,\cdot)$
Character field $\Q$
Dimension $144$
Sturm bound $320$

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Defining parameters

Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Sturm bound: \(320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1064, [\chi])\).

Total New Old
Modular forms 164 144 20
Cusp forms 156 144 12
Eisenstein series 8 0 8

Trace form

\( 144 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 144 q^{9} + O(q^{10}) \) \( 144 q + 2 q^{2} + 2 q^{4} + 2 q^{8} - 144 q^{9} - 8 q^{11} + 2 q^{14} + 26 q^{16} - 30 q^{18} + 12 q^{22} + 144 q^{25} - 28 q^{28} - 52 q^{30} - 38 q^{32} - 30 q^{36} + 2 q^{42} - 8 q^{43} + 44 q^{46} - 2 q^{50} - 80 q^{51} - 2 q^{56} - 24 q^{58} + 76 q^{60} - 10 q^{64} + 40 q^{67} - 24 q^{70} + 10 q^{72} - 88 q^{74} + 52 q^{78} + 176 q^{81} - 16 q^{84} - 40 q^{86} - 132 q^{88} - 80 q^{91} + 44 q^{92} + 106 q^{98} + 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1064, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1064, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1064, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 2}\)