Properties

Label 297.2.e
Level $297$
Weight $2$
Character orbit 297.e
Rep. character $\chi_{297}(100,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $20$
Newform subspaces $5$
Sturm bound $72$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 297.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 5 \)
Sturm bound: \(72\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(297, [\chi])\).

Total New Old
Modular forms 84 20 64
Cusp forms 60 20 40
Eisenstein series 24 0 24

Trace form

\( 20 q - 10 q^{4} + 3 q^{5} - 2 q^{7} + 12 q^{8} + 4 q^{11} - 2 q^{13} - 6 q^{14} - 10 q^{16} + 12 q^{17} + 4 q^{19} - 6 q^{20} + 6 q^{23} - 7 q^{25} - 48 q^{26} + 16 q^{28} - 12 q^{29} - 5 q^{31} - 12 q^{32}+ \cdots - 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(297, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
297.2.e.a 297.e 9.c $2$ $2.372$ \(\Q(\sqrt{-3}) \) None 99.2.e.c \(-2\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-2\zeta_{6}q^{5}+\cdots\)
297.2.e.b 297.e 9.c $2$ $2.372$ \(\Q(\sqrt{-3}) \) None 99.2.e.b \(0\) \(0\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{4}-3\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}+\cdots\)
297.2.e.c 297.e 9.c $2$ $2.372$ \(\Q(\sqrt{-3}) \) None 99.2.e.a \(1\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-4+\cdots)q^{7}+\cdots\)
297.2.e.d 297.e 9.c $6$ $2.372$ \(\Q(\zeta_{18})\) None 99.2.e.d \(0\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta_{5}+\beta_{4}+\cdots-\beta_{2})q^{2}+\cdots+\beta_{5} q^{4}+\cdots\)
297.2.e.e 297.e 9.c $8$ $2.372$ 8.0.508277025.1 None 99.2.e.e \(1\) \(0\) \(4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}+\beta _{6})q^{2}+(\beta _{3}+3\beta _{5})q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(297, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(297, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)