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Properties

Label 294.2.f
Level $294$
Weight $2$
Character orbit 294.f
Rep. character $\chi_{294}(215,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $3$
Sturm bound $112$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 294.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(112\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(294, [\chi])\).

Total New Old
Modular forms 144 28 116
Cusp forms 80 28 52
Eisenstein series 64 0 64

Trace form

\( 28 q + 14 q^{4} + 10 q^{9} + O(q^{10}) \) \( 28 q + 14 q^{4} + 10 q^{9} + 6 q^{10} - 12 q^{15} - 14 q^{16} + 4 q^{18} - 12 q^{19} - 20 q^{22} - 6 q^{24} - 24 q^{25} - 4 q^{30} + 6 q^{31} + 18 q^{33} + 20 q^{36} + 28 q^{37} - 4 q^{39} + 6 q^{40} - 32 q^{43} + 12 q^{46} - 12 q^{51} - 12 q^{52} - 18 q^{54} - 8 q^{57} - 2 q^{58} - 6 q^{60} - 28 q^{64} - 20 q^{67} - 4 q^{72} - 24 q^{73} + 32 q^{78} - 54 q^{79} + 18 q^{81} + 24 q^{82} + 72 q^{85} + 18 q^{87} - 10 q^{88} + 24 q^{94} - 6 q^{96} - 112 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(294, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
294.2.f.a 294.f 21.g $4$ $2.348$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
294.2.f.b 294.f 21.g $8$ $2.348$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}+\zeta_{24}^{4})q^{2}-\zeta_{24}^{6}q^{3}+(1+\cdots)q^{4}+\cdots\)
294.2.f.c 294.f 21.g $16$ $2.348$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{48}^{4}-\zeta_{48}^{12})q^{2}+(\zeta_{48}+\zeta_{48}^{3}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(294, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)