Properties

Label 3150.2.u
Level 3150
Weight 2
Character orbit u
Rep. character \(\chi_{3150}(551,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 304
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.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 1488 304 1184
Cusp forms 1392 304 1088
Eisenstein series 96 0 96

Trace form

\(304q \) \(\mathstrut +\mathstrut 152q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(304q \) \(\mathstrut +\mathstrut 152q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 152q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut -\mathstrut 4q^{18} \) \(\mathstrut -\mathstrut 2q^{21} \) \(\mathstrut +\mathstrut 6q^{24} \) \(\mathstrut -\mathstrut 12q^{26} \) \(\mathstrut -\mathstrut 2q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 42q^{33} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 2q^{42} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 12q^{44} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 18q^{47} \) \(\mathstrut -\mathstrut 14q^{49} \) \(\mathstrut -\mathstrut 4q^{51} \) \(\mathstrut +\mathstrut 36q^{53} \) \(\mathstrut +\mathstrut 18q^{54} \) \(\mathstrut +\mathstrut 6q^{57} \) \(\mathstrut +\mathstrut 12q^{58} \) \(\mathstrut +\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 36q^{62} \) \(\mathstrut +\mathstrut 38q^{63} \) \(\mathstrut -\mathstrut 304q^{64} \) \(\mathstrut +\mathstrut 14q^{67} \) \(\mathstrut -\mathstrut 36q^{68} \) \(\mathstrut -\mathstrut 42q^{69} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 16q^{78} \) \(\mathstrut +\mathstrut 20q^{79} \) \(\mathstrut -\mathstrut 14q^{81} \) \(\mathstrut +\mathstrut 2q^{84} \) \(\mathstrut -\mathstrut 48q^{87} \) \(\mathstrut -\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 12q^{91} \) \(\mathstrut +\mathstrut 30q^{92} \) \(\mathstrut -\mathstrut 38q^{93} \) \(\mathstrut +\mathstrut 6q^{96} \) \(\mathstrut -\mathstrut 6q^{97} \) \(\mathstrut +\mathstrut 24q^{98} \) \(\mathstrut +\mathstrut 10q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)