Properties

Label 150.2.c
Level 150
Weight 2
Character orbit c
Rep. character \(\chi_{150}(49,\cdot)\)
Character field \(\Q\)
Dimension 2
Newforms 1
Sturm bound 60
Trace bound 0

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Defining parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 150.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(150, [\chi])\).

Total New Old
Modular forms 42 2 40
Cusp forms 18 2 16
Eisenstein series 24 0 24

Trace form

\(2q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 2q^{16} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut +\mathstrut 2q^{24} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut +\mathstrut 12q^{34} \) \(\mathstrut +\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 12q^{51} \) \(\mathstrut +\mathstrut 2q^{54} \) \(\mathstrut +\mathstrut 8q^{56} \) \(\mathstrut -\mathstrut 20q^{61} \) \(\mathstrut -\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 4q^{74} \) \(\mathstrut -\mathstrut 8q^{76} \) \(\mathstrut -\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 2q^{81} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 8q^{86} \) \(\mathstrut -\mathstrut 36q^{89} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut -\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(150, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
150.2.c.a \(2\) \(1.198\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)