Properties

Label 1470.2.bm
Level $1470$
Weight $2$
Character orbit 1470.bm
Rep. character $\chi_{1470}(59,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1344$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.bm (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 735 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1470, [\chi])\).

Total New Old
Modular forms 4128 1344 2784
Cusp forms 3936 1344 2592
Eisenstein series 192 0 192

Trace form

\( 1344q + 112q^{4} + 14q^{6} - 16q^{9} + O(q^{10}) \) \( 1344q + 112q^{4} + 14q^{6} - 16q^{9} + 6q^{10} - 12q^{15} + 112q^{16} + 24q^{19} - 10q^{21} + 6q^{24} - 2q^{25} + 6q^{30} + 12q^{31} - 10q^{36} + 20q^{39} + 22q^{40} + 120q^{45} - 156q^{46} + 72q^{49} + 12q^{51} + 322q^{55} + 6q^{60} - 52q^{61} - 224q^{64} - 48q^{66} + 24q^{70} + 96q^{75} + 28q^{79} - 48q^{81} + 68q^{84} + 16q^{85} + 42q^{90} - 128q^{91} + 16q^{94} - 6q^{96} - 192q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1470, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1470, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)