Properties

Label 1470.2.be
Level $1470$
Weight $2$
Character orbit 1470.be
Rep. character $\chi_{1470}(41,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $432$
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.be (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
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 432 1632
Cusp forms 1968 432 1536
Eisenstein series 96 0 96

Trace form

\( 432q + 72q^{4} + 14q^{6} - 12q^{7} + 10q^{9} + O(q^{10}) \) \( 432q + 72q^{4} + 14q^{6} - 12q^{7} + 10q^{9} - 72q^{16} + 16q^{18} + 16q^{21} - 72q^{25} - 84q^{27} + 12q^{28} + 4q^{30} - 10q^{36} + 116q^{37} + 24q^{39} - 80q^{42} - 40q^{43} + 60q^{46} + 56q^{49} + 24q^{51} + 84q^{52} - 40q^{57} + 40q^{58} + 252q^{61} - 20q^{63} + 72q^{64} + 88q^{67} - 56q^{69} + 12q^{70} - 16q^{72} + 32q^{78} + 24q^{79} + 30q^{81} - 16q^{84} + 112q^{87} - 80q^{91} - 8q^{93} - 112q^{94} + 256q^{99} + O(q^{100}) \)

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

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