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Properties

Label 294.3.g
Level $294$
Weight $3$
Character orbit 294.g
Rep. character $\chi_{294}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $5$
Sturm bound $168$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 294.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(168\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 256 28 228
Cusp forms 192 28 164
Eisenstein series 64 0 64

Trace form

\( 28 q - 6 q^{3} - 28 q^{4} - 12 q^{5} + 42 q^{9} + O(q^{10}) \) \( 28 q - 6 q^{3} - 28 q^{4} - 12 q^{5} + 42 q^{9} + 24 q^{10} + 12 q^{11} + 12 q^{12} - 24 q^{15} - 56 q^{16} + 48 q^{17} + 42 q^{19} + 16 q^{22} - 32 q^{23} + 66 q^{25} - 96 q^{26} - 80 q^{29} + 48 q^{30} - 102 q^{31} + 36 q^{33} - 168 q^{36} - 26 q^{37} - 24 q^{38} - 90 q^{39} - 48 q^{40} + 412 q^{43} + 24 q^{44} - 36 q^{45} + 96 q^{46} + 132 q^{47} + 32 q^{50} + 72 q^{51} - 12 q^{52} - 48 q^{53} - 516 q^{57} - 176 q^{58} + 24 q^{59} + 24 q^{60} + 72 q^{61} + 224 q^{64} + 228 q^{65} + 286 q^{67} - 96 q^{68} - 440 q^{71} + 66 q^{73} - 384 q^{74} - 66 q^{75} - 288 q^{78} - 426 q^{79} + 48 q^{80} - 126 q^{81} - 48 q^{82} + 1680 q^{85} - 40 q^{86} - 16 q^{88} + 72 q^{89} + 128 q^{92} + 342 q^{93} + 24 q^{94} + 140 q^{95} + 72 q^{99} + O(q^{100}) \)

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.g.a 294.g 7.d $4$ $8.011$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-6\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
294.3.g.b 294.g 7.d $4$ $8.011$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-6\) \(12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
294.3.g.c 294.g 7.d $4$ $8.011$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(6\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-2+\cdots)q^{5}+\cdots\)
294.3.g.d 294.g 7.d $8$ $8.011$ 8.0.339738624.1 None \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{5})q^{2}+(-2-\beta _{4})q^{3}+2\beta _{4}q^{4}+\cdots\)
294.3.g.e 294.g 7.d $8$ $8.011$ 8.0.339738624.1 None \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}+\beta _{5})q^{2}+(2+\beta _{4})q^{3}+2\beta _{4}q^{4}+\cdots\)

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

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