Properties

Label 770.2.br
Level $770$
Weight $2$
Character orbit 770.br
Rep. character $\chi_{770}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $384$
Newform subspaces $2$
Sturm bound $288$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.br (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 2 \)
Sturm bound: \(288\)
Trace bound: \(2\)
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 384 832
Cusp forms 1088 384 704
Eisenstein series 128 0 128

Trace form

\( 384q + 48q^{4} + 12q^{5} + 36q^{9} + O(q^{10}) \) \( 384q + 48q^{4} + 12q^{5} + 36q^{9} - 2q^{11} + 6q^{14} + 12q^{15} + 48q^{16} - 20q^{25} + 12q^{26} + 36q^{31} - 30q^{35} - 112q^{36} - 20q^{39} + 30q^{40} - 22q^{44} - 12q^{45} - 8q^{49} - 60q^{51} + 8q^{56} + 4q^{60} - 60q^{61} - 96q^{64} - 192q^{66} + 54q^{70} - 80q^{71} + 60q^{75} + 18q^{80} - 36q^{81} + 20q^{85} - 36q^{86} - 120q^{89} + 2q^{91} + 150q^{94} + 90q^{95} - 44q^{99} + O(q^{100}) \)

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.br.a \(192\) \(6.148\) None \(-24\) \(0\) \(6\) \(6\)
770.2.br.b \(192\) \(6.148\) None \(24\) \(0\) \(6\) \(-6\)

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

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