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Properties

Label 2070.2.x
Level $2070$
Weight $2$
Character orbit 2070.x
Rep. character $\chi_{2070}(47,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $528$
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.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 1760 528 1232
Cusp forms 1696 528 1168
Eisenstein series 64 0 64

Trace form

\( 528 q + O(q^{10}) \) \( 528 q + 48 q^{11} + 24 q^{15} + 264 q^{16} + 16 q^{21} + 48 q^{30} - 16 q^{33} - 16 q^{36} - 72 q^{38} - 88 q^{42} - 136 q^{45} - 120 q^{47} - 96 q^{50} + 96 q^{51} - 120 q^{57} - 24 q^{58} + 64 q^{63} + 48 q^{66} + 72 q^{68} - 56 q^{75} - 24 q^{78} + 32 q^{81} + 96 q^{82} + 48 q^{85} + 144 q^{86} + 128 q^{87} + 56 q^{90} - 96 q^{91} - 88 q^{93} + 48 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)