Properties

Label 770.2.t
Level $770$
Weight $2$
Character orbit 770.t
Rep. character $\chi_{770}(131,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $2$
Sturm bound $288$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(770, [\chi])\).

Total New Old
Modular forms 304 64 240
Cusp forms 272 64 208
Eisenstein series 32 0 32

Trace form

\( 64q + 32q^{4} + 24q^{9} + O(q^{10}) \) \( 64q + 32q^{4} + 24q^{9} - 6q^{11} + 12q^{14} + 16q^{15} - 32q^{16} - 8q^{22} - 24q^{23} + 32q^{25} + 60q^{26} - 24q^{33} + 48q^{36} - 8q^{37} - 24q^{38} + 6q^{44} - 24q^{47} - 40q^{49} + 16q^{53} - 8q^{58} - 120q^{59} + 8q^{60} - 64q^{64} - 48q^{66} - 8q^{67} + 32q^{71} - 40q^{77} + 32q^{78} - 48q^{82} - 16q^{86} - 4q^{88} - 72q^{89} + 88q^{91} - 48q^{92} + 40q^{93} - 44q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(770, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
770.2.t.a \(32\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)
770.2.t.b \(32\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(770, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)