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Properties

Label 294.2.d
Level $294$
Weight $2$
Character orbit 294.d
Rep. character $\chi_{294}(293,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
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 72 12 60
Cusp forms 40 12 28
Eisenstein series 32 0 32

Trace form

\( 12 q - 12 q^{4} - 4 q^{9} + 12 q^{15} + 12 q^{16} - 16 q^{18} - 4 q^{22} + 16 q^{25} + 16 q^{30} + 4 q^{36} - 24 q^{37} + 16 q^{39} - 48 q^{43} + 24 q^{46} - 24 q^{51} - 16 q^{57} - 28 q^{58} - 12 q^{60}+ \cdots - 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
294.2.d.a 294.d 21.c $4$ $2.348$ \(\Q(\zeta_{12})\) None 42.2.f.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{2}+\beta_{3} q^{3}-q^{4}+\beta_{3} q^{5}+\cdots\)
294.2.d.b 294.d 21.c $8$ $2.348$ \(\Q(\zeta_{16})\) None 294.2.d.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{16}^{4}q^{2}+(\zeta_{16}+\zeta_{16}^{5}+\zeta_{16}^{7})q^{3}+\cdots\)

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

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