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Properties

Label 294.3.c
Level $294$
Weight $3$
Character orbit 294.c
Rep. character $\chi_{294}(97,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 294.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(294, [\chi])\).

Total New Old
Modular forms 128 12 116
Cusp forms 96 12 84
Eisenstein series 32 0 32

Trace form

\( 12 q + 24 q^{4} - 36 q^{9} + O(q^{10}) \) \( 12 q + 24 q^{4} - 36 q^{9} + 24 q^{11} + 24 q^{15} + 48 q^{16} + 32 q^{22} - 16 q^{23} - 116 q^{25} - 160 q^{29} - 48 q^{30} - 72 q^{36} + 84 q^{37} - 12 q^{39} + 348 q^{43} + 48 q^{44} + 48 q^{46} - 176 q^{50} + 144 q^{53} - 276 q^{57} + 272 q^{58} + 48 q^{60} + 96 q^{64} - 648 q^{65} - 572 q^{67} + 56 q^{71} + 144 q^{74} + 308 q^{79} + 108 q^{81} + 480 q^{85} + 304 q^{86} + 64 q^{88} - 32 q^{92} - 300 q^{93} + 232 q^{95} - 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(294, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
294.3.c.a 294.c 7.b $4$ $8.011$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+(2\beta _{2}-2\beta _{3})q^{5}+\cdots\)
294.3.c.b 294.c 7.b $8$ $8.011$ 8.0.339738624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+(\beta _{4}-2\beta _{7})q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(294, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(294, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)