Properties

Label 150.2.e
Level 150
Weight 2
Character orbit e
Rep. character \(\chi_{150}(107,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 12
Newforms 2
Sturm bound 60
Trace bound 1

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Defining parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 150.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 15 \)
Character field: \(\Q(i)\)
Newforms: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 84 12 72
Cusp forms 36 12 24
Eisenstein series 48 0 48

Trace form

\(12q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 12q^{16} \) \(\mathstrut -\mathstrut 8q^{18} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 24q^{31} \) \(\mathstrut +\mathstrut 4q^{33} \) \(\mathstrut +\mathstrut 8q^{36} \) \(\mathstrut -\mathstrut 24q^{37} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut -\mathstrut 32q^{46} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 88q^{61} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 44q^{66} \) \(\mathstrut +\mathstrut 16q^{67} \) \(\mathstrut +\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 64q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 8q^{93} \) \(\mathstrut -\mathstrut 8q^{96} \) \(\mathstrut -\mathstrut 12q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.e.a \(4\) \(1.198\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(4\) \(q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
150.2.e.b \(8\) \(1.198\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}+\zeta_{24}^{5})q^{2}+(-2\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+\cdots\)

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

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