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Properties

Label 294.2.m
Level $294$
Weight $2$
Character orbit 294.m
Rep. character $\chi_{294}(25,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $120$
Newform subspaces $4$
Sturm bound $112$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 294.m (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 4 \)
Sturm bound: \(112\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(294, [\chi])\).

Total New Old
Modular forms 720 120 600
Cusp forms 624 120 504
Eisenstein series 96 0 96

Trace form

\( 120 q + 10 q^{4} + 4 q^{5} + 4 q^{6} - 6 q^{7} + 10 q^{9} + O(q^{10}) \) \( 120 q + 10 q^{4} + 4 q^{5} + 4 q^{6} - 6 q^{7} + 10 q^{9} - 2 q^{10} + 36 q^{11} + 8 q^{13} - 8 q^{14} + 10 q^{15} + 10 q^{16} + 24 q^{17} + 32 q^{19} + 20 q^{20} - 4 q^{21} + 2 q^{22} + 4 q^{23} - 2 q^{24} + 20 q^{25} + 32 q^{26} + 6 q^{28} - 24 q^{29} + 2 q^{31} - 2 q^{33} + 8 q^{34} + 36 q^{35} - 20 q^{36} + 36 q^{37} - 44 q^{38} - 32 q^{39} - 30 q^{40} - 112 q^{41} - 50 q^{42} - 8 q^{43} - 48 q^{44} - 52 q^{45} + 4 q^{46} - 40 q^{47} - 110 q^{49} - 16 q^{50} - 104 q^{51} - 4 q^{52} - 100 q^{53} - 2 q^{54} + 14 q^{55} - 52 q^{56} + 16 q^{57} - 36 q^{58} - 92 q^{59} - 26 q^{60} - 72 q^{61} - 64 q^{62} - 20 q^{64} + 28 q^{65} - 8 q^{66} + 8 q^{67} - 4 q^{68} - 8 q^{69} + 16 q^{70} - 40 q^{71} + 96 q^{73} + 40 q^{74} + 8 q^{75} - 8 q^{76} + 112 q^{77} + 40 q^{78} + 18 q^{79} + 4 q^{80} + 10 q^{81} + 4 q^{83} + 8 q^{84} - 16 q^{85} + 104 q^{86} + 28 q^{87} + 34 q^{88} - 28 q^{89} + 4 q^{90} - 64 q^{91} - 8 q^{92} + 28 q^{94} - 188 q^{95} - 2 q^{96} + 44 q^{97} - 24 q^{98} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
294.2.m.a 294.m 49.g $24$ $2.348$ None \(-2\) \(-2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{21}]$
294.2.m.b 294.m 49.g $24$ $2.348$ None \(2\) \(2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{21}]$
294.2.m.c 294.m 49.g $36$ $2.348$ None \(-3\) \(3\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{21}]$
294.2.m.d 294.m 49.g $36$ $2.348$ None \(3\) \(-3\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{21}]$

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

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