Properties

Label 150.3.b
Level $150$
Weight $3$
Character orbit 150.b
Rep. character $\chi_{150}(149,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $90$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(90\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(150, [\chi])\).

Total New Old
Modular forms 72 12 60
Cusp forms 48 12 36
Eisenstein series 24 0 24

Trace form

\( 12q + 24q^{4} + 8q^{6} + 44q^{9} + O(q^{10}) \) \( 12q + 24q^{4} + 8q^{6} + 44q^{9} + 48q^{16} - 36q^{19} - 76q^{21} + 16q^{24} + 36q^{31} + 48q^{34} + 88q^{36} - 20q^{39} - 192q^{46} - 360q^{49} - 144q^{51} - 200q^{54} - 132q^{61} + 96q^{64} + 144q^{66} - 24q^{69} - 72q^{76} + 456q^{79} + 124q^{81} - 152q^{84} + 540q^{91} + 240q^{94} + 32q^{96} + 576q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
150.3.b.a \(4\) \(4.087\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}-2\zeta_{8}^{3})q^{3}+2q^{4}+\cdots\)
150.3.b.b \(8\) \(4.087\) 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}-\beta _{3}q^{3}+2q^{4}+(-1-\beta _{4}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)