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Properties

Label 1470.2.j
Level $1470$
Weight $2$
Character orbit 1470.j
Rep. character $\chi_{1470}(197,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $164$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 736 164 572
Cusp forms 608 164 444
Eisenstein series 128 0 128

Trace form

\( 164 q - 4 q^{3} + 4 q^{6} + O(q^{10}) \) \( 164 q - 4 q^{3} + 4 q^{6} - 4 q^{10} + 4 q^{12} - 16 q^{15} - 164 q^{16} - 8 q^{18} + 4 q^{22} - 32 q^{25} - 4 q^{27} + 12 q^{30} + 24 q^{31} + 36 q^{33} + 4 q^{36} + 8 q^{37} + 8 q^{40} - 40 q^{43} + 48 q^{45} - 32 q^{46} + 4 q^{48} - 8 q^{51} + 20 q^{55} - 24 q^{57} + 36 q^{58} + 12 q^{60} + 24 q^{61} + 8 q^{66} + 16 q^{67} + 8 q^{72} + 68 q^{73} - 60 q^{75} - 16 q^{76} + 16 q^{78} + 52 q^{81} - 48 q^{82} + 72 q^{85} + 60 q^{87} + 4 q^{88} - 48 q^{90} - 32 q^{93} - 4 q^{96} - 28 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{2}^{\mathrm{old}}(1470, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(735, [\chi])\)\(^{\oplus 2}\)