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Properties

Label 152.2.q
Level $152$
Weight $2$
Character orbit 152.q
Rep. character $\chi_{152}(9,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $30$
Newform subspaces $3$
Sturm bound $40$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 152.q (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(152, [\chi])\).

Total New Old
Modular forms 144 30 114
Cusp forms 96 30 66
Eisenstein series 48 0 48

Trace form

\( 30 q + 3 q^{3} - 9 q^{9} + O(q^{10}) \) \( 30 q + 3 q^{3} - 9 q^{9} - 6 q^{13} + 12 q^{15} + 6 q^{17} - 6 q^{19} - 6 q^{21} + 12 q^{23} + 12 q^{25} - 27 q^{27} - 12 q^{29} - 6 q^{31} - 45 q^{33} - 18 q^{35} + 12 q^{37} - 36 q^{39} - 39 q^{41} - 48 q^{43} - 18 q^{45} - 21 q^{49} + 15 q^{51} - 18 q^{53} - 36 q^{55} + 36 q^{57} + 33 q^{59} - 6 q^{61} - 6 q^{63} + 42 q^{65} + 75 q^{67} + 24 q^{69} + 54 q^{71} + 54 q^{73} + 84 q^{75} + 36 q^{77} + 108 q^{79} + 69 q^{81} - 12 q^{85} + 54 q^{87} + 36 q^{89} + 84 q^{91} + 66 q^{93} - 78 q^{95} - 69 q^{97} - 3 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
152.2.q.a 152.q 19.e $6$ $1.214$ \(\Q(\zeta_{18})\) None \(0\) \(-6\) \(6\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1+\zeta_{18}^{2}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}^{5})q^{5}+\cdots\)
152.2.q.b 152.q 19.e $6$ $1.214$ \(\Q(\zeta_{18})\) None \(0\) \(9\) \(-6\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+2\zeta_{18}^{5})q^{3}+\cdots\)
152.2.q.c 152.q 19.e $18$ $1.214$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q+(\beta _{2}-\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(152, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(152, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)