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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
294.2.m.a \(24\) \(2.348\) None \(-2\) \(-2\) \(1\) \(0\)
294.2.m.b \(24\) \(2.348\) None \(2\) \(2\) \(1\) \(0\)
294.2.m.c \(36\) \(2.348\) None \(-3\) \(3\) \(2\) \(-5\)
294.2.m.d \(36\) \(2.348\) None \(3\) \(-3\) \(0\) \(-1\)

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

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