Properties

Label 3150.2.cb
Level 3150
Weight 2
Character orbit cb
Rep. character \(\chi_{3150}(443,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 576
Sturm bound 1440

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Defining parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.cb (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 315 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 2976 576 2400
Cusp forms 2784 576 2208
Eisenstein series 192 0 192

Trace form

\(576q \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(576q \) \(\mathstrut -\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 288q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 16q^{18} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 36q^{27} \) \(\mathstrut +\mathstrut 20q^{33} \) \(\mathstrut -\mathstrut 24q^{41} \) \(\mathstrut +\mathstrut 4q^{42} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 48q^{51} \) \(\mathstrut +\mathstrut 48q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 28q^{63} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 48q^{77} \) \(\mathstrut +\mathstrut 16q^{78} \) \(\mathstrut -\mathstrut 8q^{81} \) \(\mathstrut -\mathstrut 40q^{87} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 12q^{93} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into irreducible Hecke orbits

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

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)