Properties

Label 3150.2.k
Level 3150
Weight 2
Character orbit k
Rep. character \(\chi_{3150}(1801,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 128
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.k (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1536 128 1408
Cusp forms 1344 128 1216
Eisenstein series 192 0 192

Trace form

\(128q \) \(\mathstrut -\mathstrut 64q^{4} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(128q \) \(\mathstrut -\mathstrut 64q^{4} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut +\mathstrut 24q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut -\mathstrut 8q^{44} \) \(\mathstrut -\mathstrut 8q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 32q^{53} \) \(\mathstrut -\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 4q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 16q^{61} \) \(\mathstrut -\mathstrut 8q^{62} \) \(\mathstrut +\mathstrut 128q^{64} \) \(\mathstrut +\mathstrut 40q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut -\mathstrut 32q^{71} \) \(\mathstrut -\mathstrut 12q^{73} \) \(\mathstrut +\mathstrut 8q^{74} \) \(\mathstrut +\mathstrut 24q^{76} \) \(\mathstrut -\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 32q^{79} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut -\mathstrut 48q^{83} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut -\mathstrut 8q^{89} \) \(\mathstrut -\mathstrut 36q^{91} \) \(\mathstrut +\mathstrut 16q^{92} \) \(\mathstrut +\mathstrut 28q^{94} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 48q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)