Properties

Label 1470.2.r
Level $1470$
Weight $2$
Character orbit 1470.r
Rep. character $\chi_{1470}(521,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $104$
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.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 736 104 632
Cusp forms 608 104 504
Eisenstein series 128 0 128

Trace form

\( 104q + 52q^{4} - 10q^{9} + O(q^{10}) \) \( 104q + 52q^{4} - 10q^{9} + 16q^{15} - 52q^{16} + 8q^{18} + 6q^{24} - 52q^{25} + 2q^{30} - 24q^{31} + 24q^{33} - 20q^{36} - 40q^{37} + 12q^{39} + 128q^{43} - 6q^{45} + 4q^{46} - 4q^{51} + 24q^{52} + 36q^{54} + 104q^{57} - 24q^{58} + 8q^{60} + 60q^{61} - 104q^{64} + 48q^{66} + 56q^{67} - 8q^{72} - 96q^{78} + 88q^{79} - 14q^{81} - 96q^{85} - 72q^{87} + 60q^{93} - 48q^{94} + 6q^{96} + 64q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)