Properties

Label 490.2.q
Level $490$
Weight $2$
Character orbit 490.q
Rep. character $\chi_{490}(11,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $240$
Newform subspaces $4$
Sturm bound $168$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.q (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 4 \)
Sturm bound: \(168\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(490, [\chi])\).

Total New Old
Modular forms 1056 240 816
Cusp forms 960 240 720
Eisenstein series 96 0 96

Trace form

\( 240q + 20q^{4} - 2q^{5} + 10q^{6} + 8q^{7} + 40q^{9} + O(q^{10}) \) \( 240q + 20q^{4} - 2q^{5} + 10q^{6} + 8q^{7} + 40q^{9} - 2q^{10} + 2q^{11} - 2q^{14} + 20q^{16} - 4q^{17} + 8q^{18} - 6q^{19} + 4q^{20} + 18q^{21} - 8q^{22} + 96q^{23} + 2q^{24} + 20q^{25} + 24q^{26} + 60q^{27} - 4q^{28} - 6q^{29} + 2q^{30} + 8q^{31} - 24q^{33} - 16q^{34} + 8q^{35} - 38q^{36} - 4q^{37} - 64q^{38} + 52q^{39} - 2q^{40} - 72q^{41} - 32q^{42} + 24q^{43} - 26q^{44} - 4q^{45} - 76q^{46} - 8q^{47} - 90q^{49} - 92q^{51} + 28q^{52} - 92q^{53} - 70q^{54} - 16q^{55} - 30q^{56} - 8q^{57} - 104q^{58} - 38q^{59} + 122q^{61} - 8q^{62} + 48q^{63} - 40q^{64} + 2q^{65} + 8q^{67} + 52q^{68} + 92q^{69} - 6q^{70} - 64q^{71} + 8q^{72} + 56q^{73} + 36q^{74} + 12q^{76} + 92q^{77} - 32q^{78} + 8q^{79} + 12q^{80} - 46q^{81} - 16q^{82} + 116q^{83} - 8q^{85} + 10q^{86} - 200q^{87} + 32q^{88} - 30q^{89} + 20q^{90} - 30q^{91} - 24q^{92} + 20q^{93} + 72q^{94} + 8q^{95} + 2q^{96} - 176q^{97} + 32q^{98} + 108q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(490, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
490.2.q.a \(48\) \(3.913\) None \(4\) \(8\) \(4\) \(0\)
490.2.q.b \(60\) \(3.913\) None \(-5\) \(-8\) \(5\) \(4\)
490.2.q.c \(60\) \(3.913\) None \(-5\) \(0\) \(-5\) \(1\)
490.2.q.d \(72\) \(3.913\) None \(6\) \(0\) \(-6\) \(3\)

Decomposition of \(S_{2}^{\mathrm{old}}(490, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(490, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)