Properties

Label 1350.2.m
Level 1350
Weight 2
Character orbit m
Rep. character \(\chi_{1350}(109,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 160
Sturm bound 540

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Defining parameters

Level: \( N \) = \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1350.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1350, [\chi])\).

Total New Old
Modular forms 1128 160 968
Cusp forms 1032 160 872
Eisenstein series 96 0 96

Trace form

\(160q \) \(\mathstrut +\mathstrut 40q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(160q \) \(\mathstrut +\mathstrut 40q^{4} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 40q^{16} \) \(\mathstrut +\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 20q^{22} \) \(\mathstrut -\mathstrut 26q^{25} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut +\mathstrut 40q^{37} \) \(\mathstrut +\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 12q^{46} \) \(\mathstrut -\mathstrut 100q^{49} \) \(\mathstrut -\mathstrut 58q^{55} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 40q^{64} \) \(\mathstrut +\mathstrut 40q^{67} \) \(\mathstrut +\mathstrut 98q^{70} \) \(\mathstrut +\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 144q^{85} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut -\mathstrut 20q^{91} \) \(\mathstrut -\mathstrut 16q^{94} \) \(\mathstrut +\mathstrut 10q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1350, [\chi])\) into irreducible Hecke orbits

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1350, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1350, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 2}\)