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Properties

Label 2070.2.bj
Level $2070$
Weight $2$
Character orbit 2070.bj
Rep. character $\chi_{2070}(37,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $1200$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2070.bj (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2070, [\chi])\).

Total New Old
Modular forms 8960 1200 7760
Cusp forms 8320 1200 7120
Eisenstein series 640 0 640

Trace form

\( 1200 q + O(q^{10}) \) \( 1200 q - 16 q^{13} + 120 q^{16} - 88 q^{23} + 32 q^{25} - 8 q^{26} - 44 q^{28} - 8 q^{31} - 8 q^{35} + 88 q^{37} + 24 q^{41} - 24 q^{46} - 64 q^{47} + 8 q^{50} - 16 q^{52} + 32 q^{55} + 44 q^{56} + 176 q^{61} - 32 q^{62} - 72 q^{70} + 384 q^{71} + 40 q^{73} + 40 q^{77} - 24 q^{82} + 28 q^{85} + 44 q^{86} - 92 q^{95} + 132 q^{97} + 120 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2070, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2070, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)