Properties

Label 294.2.e
Level $294$
Weight $2$
Character orbit 294.e
Rep. character $\chi_{294}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $6$
Sturm bound $112$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 294.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(112\)
Trace bound: \(5\)
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 12 132
Cusp forms 80 12 68
Eisenstein series 64 0 64

Trace form

\( 12q - 6q^{4} + 4q^{5} + 4q^{6} - 6q^{9} + O(q^{10}) \) \( 12q - 6q^{4} + 4q^{5} + 4q^{6} - 6q^{9} - 2q^{10} + 8q^{11} + 8q^{13} - 4q^{15} - 6q^{16} - 4q^{17} + 4q^{19} - 8q^{20} + 4q^{22} - 12q^{23} - 2q^{24} - 20q^{25} + 4q^{26} + 8q^{29} - 8q^{30} + 2q^{31} - 2q^{33} + 8q^{34} + 12q^{36} + 28q^{37} + 12q^{38} + 24q^{39} - 2q^{40} - 16q^{43} + 8q^{44} + 4q^{45} - 12q^{46} - 12q^{47} - 64q^{50} - 4q^{52} + 20q^{53} - 2q^{54} - 28q^{55} - 24q^{57} + 22q^{58} - 8q^{59} + 2q^{60} - 16q^{61} - 8q^{62} + 12q^{64} + 4q^{65} - 8q^{66} - 4q^{67} - 4q^{68} - 8q^{69} + 56q^{71} + 12q^{73} + 20q^{74} + 8q^{75} - 8q^{76} + 14q^{79} + 4q^{80} - 6q^{81} + 32q^{83} - 24q^{85} + 4q^{86} + 14q^{87} - 2q^{88} + 4q^{90} + 24q^{92} + 20q^{93} - 44q^{95} - 2q^{96} - 12q^{97} - 16q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
294.2.e.a \(2\) \(2.348\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(-2\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
294.2.e.b \(2\) \(2.348\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
294.2.e.c \(2\) \(2.348\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(2\) \(0\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
294.2.e.d \(2\) \(2.348\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(4\) \(0\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
294.2.e.e \(2\) \(2.348\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-4\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
294.2.e.f \(2\) \(2.348\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(3\) \(0\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)