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Properties

Label 468.2.be
Level $468$
Weight $2$
Character orbit 468.be
Rep. character $\chi_{468}(49,\cdot)$
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.be (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

\( 28 q + 2 q^{9} + O(q^{10}) \) \( 28 q + 2 q^{9} - q^{13} - 8 q^{17} - 3 q^{19} + 6 q^{21} - 8 q^{23} + 14 q^{25} + 5 q^{29} - 6 q^{31} + 27 q^{33} + 19 q^{35} + 3 q^{37} - 5 q^{39} - 4 q^{43} + 30 q^{45} + 33 q^{47} - 32 q^{49} + 19 q^{51} - 36 q^{53} - 3 q^{57} - 24 q^{59} - 14 q^{61} - 33 q^{63} + 22 q^{65} - 5 q^{69} - 12 q^{71} + 44 q^{75} - 12 q^{77} + 7 q^{79} + 2 q^{81} - 51 q^{83} + 18 q^{85} - 34 q^{87} - 33 q^{89} - 3 q^{91} - 3 q^{93} - 12 q^{95} - 27 q^{99} + O(q^{100}) \)

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.be.a 468.be 117.r $2$ $3.737$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(2-4\zeta_{6})q^{7}+\cdots\)
468.2.be.b 468.be 117.r $6$ $3.737$ 6.0.954288.1 None \(0\) \(1\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{4}q^{3}+(-1+\beta _{2})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
468.2.be.c 468.be 117.r $20$ $3.737$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-1\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{11}q^{3}+(-\beta _{1}-\beta _{5}+\beta _{9}+\beta _{12}+\cdots)q^{5}+\cdots\)

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

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