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Properties

Label 294.3.k
Level $294$
Weight $3$
Character orbit 294.k
Rep. character $\chi_{294}(13,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $120$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 294.k (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 696 120 576
Cusp forms 648 120 528
Eisenstein series 48 0 48

Trace form

\( 120 q - 40 q^{4} - 8 q^{7} + 60 q^{9} + O(q^{10}) \) \( 120 q - 40 q^{4} - 8 q^{7} + 60 q^{9} - 116 q^{11} + 24 q^{14} - 60 q^{15} - 80 q^{16} + 196 q^{17} + 56 q^{20} - 12 q^{21} + 128 q^{22} - 32 q^{23} + 60 q^{25} - 224 q^{26} - 16 q^{28} - 80 q^{29} + 304 q^{35} + 120 q^{36} + 20 q^{37} + 280 q^{38} + 240 q^{39} + 112 q^{40} + 392 q^{41} + 120 q^{42} + 48 q^{43} + 160 q^{44} + 84 q^{45} + 96 q^{46} - 532 q^{47} - 36 q^{49} - 128 q^{50} - 120 q^{51} - 216 q^{53} + 532 q^{55} - 176 q^{56} + 72 q^{57} - 160 q^{58} - 1008 q^{59} - 120 q^{60} - 364 q^{61} - 392 q^{62} + 24 q^{63} - 160 q^{64} - 280 q^{65} - 88 q^{67} - 296 q^{70} + 184 q^{71} - 252 q^{73} + 288 q^{74} + 396 q^{77} - 240 q^{78} - 200 q^{79} - 180 q^{81} + 364 q^{83} - 24 q^{84} + 208 q^{85} - 664 q^{86} + 252 q^{87} - 304 q^{88} + 1036 q^{89} + 280 q^{91} - 64 q^{92} + 168 q^{93} + 112 q^{94} + 472 q^{95} + 192 q^{98} - 72 q^{99} + O(q^{100}) \)

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.k.a 294.k 49.f $120$ $8.011$ None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{14}]$

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

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