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Properties

Label 304.2.be
Level $304$
Weight $2$
Character orbit 304.be
Rep. character $\chi_{304}(15,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $60$
Newform subspaces $4$
Sturm bound $80$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.be (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 4 \)
Sturm bound: \(80\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(304, [\chi])\).

Total New Old
Modular forms 276 60 216
Cusp forms 204 60 144
Eisenstein series 72 0 72

Trace form

\( 60 q + 18 q^{9} + O(q^{10}) \) \( 60 q + 18 q^{9} - 12 q^{13} - 12 q^{21} + 18 q^{33} - 54 q^{41} + 30 q^{49} + 36 q^{53} + 12 q^{61} - 108 q^{65} - 96 q^{73} - 72 q^{77} - 126 q^{81} - 72 q^{85} - 36 q^{89} - 24 q^{93} - 18 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
304.2.be.a 304.be 76.k $12$ $2.427$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$ \(q+(-\beta _{1}+\beta _{7})q^{3}+(1+2\beta _{4}-\beta _{6}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.b 304.be 76.k $12$ $2.427$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$ \(q+(\beta _{3}-\beta _{5}-\beta _{8})q^{3}+(1+\beta _{2}-2\beta _{4}+\cdots)q^{5}+\cdots\)
304.2.be.c 304.be 76.k $18$ $2.427$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{18}]$ \(q-\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)
304.2.be.d 304.be 76.k $18$ $2.427$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(9\) $\mathrm{SU}(2)[C_{18}]$ \(q+\beta _{7}q^{3}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{8}-\beta _{9}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)