Properties

Label 770.2.bm
Level $770$
Weight $2$
Character orbit 770.bm
Rep. character $\chi_{770}(61,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $256$
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.bm (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 1216 256 960
Cusp forms 1088 256 832
Eisenstein series 128 0 128

Trace form

\( 256q - 32q^{4} - 44q^{9} + O(q^{10}) \) \( 256q - 32q^{4} - 44q^{9} + 6q^{11} - 2q^{14} + 24q^{15} + 32q^{16} + 60q^{17} + 8q^{22} + 24q^{23} - 32q^{25} + 60q^{26} - 40q^{29} + 24q^{33} - 48q^{36} + 8q^{37} + 24q^{38} - 20q^{39} - 40q^{42} - 6q^{44} + 24q^{47} + 60q^{49} + 60q^{51} + 24q^{53} + 8q^{58} + 120q^{59} - 8q^{60} - 200q^{63} + 64q^{64} + 48q^{66} - 32q^{67} - 60q^{68} + 128q^{71} - 40q^{72} - 180q^{73} - 40q^{74} - 60q^{77} - 192q^{78} - 60q^{79} + 60q^{81} - 72q^{82} - 80q^{84} + 16q^{86} - 16q^{88} - 48q^{89} - 98q^{91} - 72q^{92} - 100q^{93} + 90q^{94} - 116q^{99} + O(q^{100}) \)

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.bm.a \(128\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)
770.2.bm.b \(128\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)

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

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