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Properties

Label 468.2.bj
Level $468$
Weight $2$
Character orbit 468.bj
Rep. character $\chi_{468}(121,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
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.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
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 28 152
Cusp forms 156 28 128
Eisenstein series 24 0 24

Trace form

\( 28 q + 2 q^{9} + O(q^{10}) \) \( 28 q + 2 q^{9} - q^{13} - 6 q^{15} - 8 q^{17} - 3 q^{19} - 6 q^{21} + 4 q^{23} + 14 q^{25} - 10 q^{29} + 6 q^{31} - 12 q^{33} + 19 q^{35} + 3 q^{37} + 28 q^{39} - 12 q^{41} + 2 q^{43} + 15 q^{45} - 33 q^{47} + 16 q^{49} + 19 q^{51} - 36 q^{53} + 3 q^{57} + 7 q^{61} - 12 q^{63} - 11 q^{65} - 21 q^{67} - 8 q^{69} - 12 q^{71} - 16 q^{75} - 12 q^{77} + 7 q^{79} - 34 q^{81} + 51 q^{83} + 53 q^{87} - 33 q^{89} - 3 q^{91} + 27 q^{93} + 24 q^{95} + 3 q^{97} + 27 q^{99} + O(q^{100}) \)

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.bj.a 468.bj 117.l $2$ $3.737$ \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-3\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{3}+(-1-\zeta_{6})q^{5}+(2+2\zeta_{6})q^{7}+\cdots\)
468.2.bj.b 468.bj 117.l $6$ $3.737$ 6.0.954288.1 None \(0\) \(-2\) \(9\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{4})q^{3}+(1-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
468.2.bj.c 468.bj 117.l $20$ $3.737$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-1\) \(-6\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{11})q^{3}+(\beta _{1}+\beta _{5}-\beta _{9}+\cdots)q^{5}+\cdots\)

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

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