Properties

Label 1470.2.bj
Level $1470$
Weight $2$
Character orbit 1470.bj
Rep. character $\chi_{1470}(113,\cdot)$
Character field $\Q(\zeta_{28})$
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.bj (of order \(28\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 735 \)
Character field: \(\Q(\zeta_{28})\)
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

\( 1344q - 20q^{6} + 4q^{7} + O(q^{10}) \) \( 1344q - 20q^{6} + 4q^{7} - 8q^{10} - 24q^{15} + 224q^{16} + 20q^{22} + 4q^{28} + 24q^{30} + 32q^{31} + 40q^{33} + 20q^{36} + 108q^{42} - 64q^{43} - 56q^{45} + 120q^{46} + 8q^{55} + 92q^{57} - 140q^{58} + 160q^{61} - 4q^{63} + 32q^{67} - 40q^{70} + 88q^{73} - 4q^{75} - 32q^{76} - 20q^{81} - 32q^{82} + 48q^{85} + 40q^{87} - 8q^{88} + 28q^{90} + 176q^{91} + 260q^{93} - 8q^{96} - 40q^{97} + O(q^{100}) \)

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

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