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Properties

Label 468.2.i
Level $468$
Weight $2$
Character orbit 468.i
Rep. character $\chi_{468}(157,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $24$
Newform subspaces $3$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 468.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(468, [\chi])\).

Total New Old
Modular forms 180 24 156
Cusp forms 156 24 132
Eisenstein series 24 0 24

Trace form

\( 24 q + 6 q^{5} + 4 q^{9} + O(q^{10}) \) \( 24 q + 6 q^{5} + 4 q^{9} + 2 q^{11} + 2 q^{15} - 8 q^{17} + 12 q^{19} + 14 q^{21} + 2 q^{23} - 6 q^{25} - 18 q^{27} - 4 q^{29} + 6 q^{31} + 14 q^{33} + 36 q^{35} - 12 q^{37} - 2 q^{41} - 6 q^{43} + 4 q^{45} - 4 q^{47} - 24 q^{49} - 16 q^{51} - 8 q^{53} - 36 q^{55} + 32 q^{57} + 10 q^{59} - 12 q^{61} - 12 q^{63} + 8 q^{65} + 18 q^{69} + 12 q^{73} + 28 q^{75} - 22 q^{77} + 12 q^{79} - 20 q^{81} + 24 q^{83} - 6 q^{87} - 8 q^{89} - 72 q^{93} - 32 q^{95} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(468, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
468.2.i.a 468.i 9.c $2$ $3.737$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
468.2.i.b 468.i 9.c $10$ $3.737$ 10.0.\(\cdots\).1 None \(0\) \(-3\) \(7\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(2-\beta _{1}-\beta _{2}+2\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
468.2.i.c 468.i 9.c $12$ $3.737$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{5}-\beta _{7})q^{3}+\beta _{1}q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(468, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(468, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 2}\)