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Properties

Label 152.4.o
Level $152$
Weight $4$
Character orbit 152.o
Rep. character $\chi_{152}(27,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $116$
Newform subspaces $2$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 152.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(152, [\chi])\).

Total New Old
Modular forms 124 124 0
Cusp forms 116 116 0
Eisenstein series 8 8 0

Trace form

\( 116 q - 3 q^{2} - 6 q^{3} - 7 q^{4} - 23 q^{6} + 484 q^{9} + 96 q^{10} - 8 q^{11} + 120 q^{14} - 67 q^{16} - 2 q^{17} - 28 q^{19} + 576 q^{20} - 27 q^{22} - 11 q^{24} + 1248 q^{25} + 24 q^{26} + 94 q^{28}+ \cdots + 1088 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
152.4.o.a 152.o 152.o $4$ $8.968$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) 152.4.o.a \(0\) \(-30\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+2\beta _{1}q^{2}+(-5+\beta _{1}-5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots\)
152.4.o.b 152.o 152.o $112$ $8.968$ None 152.4.o.b \(-3\) \(24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$