Properties

Label 1470.2.bc
Level $1470$
Weight $2$
Character orbit 1470.bc
Rep. character $\chi_{1470}(209,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $672$
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.bc (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 735 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 2064 672 1392
Cusp forms 1968 672 1296
Eisenstein series 96 0 96

Trace form

\( 672q - 112q^{4} - 14q^{6} + 10q^{9} + O(q^{10}) \) \( 672q - 112q^{4} - 14q^{6} + 10q^{9} + 12q^{15} - 112q^{16} + 16q^{21} - 4q^{25} + 12q^{30} + 10q^{36} + 40q^{39} + 14q^{40} - 126q^{45} - 60q^{46} + 72q^{49} + 24q^{51} + 14q^{55} + 12q^{60} - 56q^{61} - 112q^{64} + 18q^{70} + 56q^{79} - 54q^{81} - 68q^{84} - 16q^{85} - 42q^{90} + 80q^{91} - 112q^{94} + 192q^{99} + O(q^{100}) \)

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

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