Properties

Label 3150.2.cr
Level 3150
Weight 2
Character orbit cr
Rep. character \(\chi_{3150}(361,\cdot)\)
Character field \(\Q(\zeta_{15})\)
Dimension 800
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.cr (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 175 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 5888 800 5088
Cusp forms 5632 800 4832
Eisenstein series 256 0 256

Trace form

\(800q \) \(\mathstrut +\mathstrut 100q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(800q \) \(\mathstrut +\mathstrut 100q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 100q^{16} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut -\mathstrut 32q^{22} \) \(\mathstrut -\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 48q^{26} \) \(\mathstrut -\mathstrut 2q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 16q^{34} \) \(\mathstrut -\mathstrut 24q^{35} \) \(\mathstrut -\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 72q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 12q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 16q^{50} \) \(\mathstrut -\mathstrut 16q^{53} \) \(\mathstrut +\mathstrut 24q^{55} \) \(\mathstrut +\mathstrut 8q^{58} \) \(\mathstrut +\mathstrut 8q^{61} \) \(\mathstrut -\mathstrut 200q^{64} \) \(\mathstrut +\mathstrut 18q^{65} \) \(\mathstrut +\mathstrut 32q^{67} \) \(\mathstrut -\mathstrut 40q^{68} \) \(\mathstrut +\mathstrut 46q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 36q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut -\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut -\mathstrut 64q^{82} \) \(\mathstrut +\mathstrut 40q^{83} \) \(\mathstrut +\mathstrut 12q^{85} \) \(\mathstrut -\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 54q^{89} \) \(\mathstrut -\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 32q^{92} \) \(\mathstrut +\mathstrut 32q^{94} \) \(\mathstrut -\mathstrut 32q^{95} \) \(\mathstrut +\mathstrut 132q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)