Properties

Label 770.2.ba
Level $770$
Weight $2$
Character orbit 770.ba
Rep. character $\chi_{770}(169,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $144$
Newform subspaces $3$
Sturm bound $288$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.ba (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 3 \)
Sturm bound: \(288\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 608 144 464
Cusp forms 544 144 400
Eisenstein series 64 0 64

Trace form

\( 144q + 36q^{4} - 4q^{5} + 56q^{9} + O(q^{10}) \) \( 144q + 36q^{4} - 4q^{5} + 56q^{9} + 4q^{11} - 16q^{15} - 36q^{16} + 32q^{19} + 4q^{20} + 40q^{21} + 24q^{25} + 16q^{29} + 44q^{30} - 8q^{31} - 16q^{34} - 36q^{36} - 12q^{39} - 4q^{44} - 40q^{45} - 56q^{46} + 36q^{49} - 24q^{50} + 28q^{51} - 68q^{55} + 8q^{59} - 24q^{60} - 64q^{61} + 36q^{64} - 32q^{65} + 8q^{66} - 32q^{69} + 8q^{70} + 64q^{71} + 8q^{74} - 8q^{75} - 32q^{76} - 4q^{80} + 24q^{81} + 20q^{84} + 12q^{85} - 56q^{86} + 144q^{89} + 60q^{90} - 36q^{91} - 32q^{94} + 16q^{95} - 172q^{99} + O(q^{100}) \)

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.ba.a \(8\) \(6.148\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{20}^{7}q^{2}+(2\zeta_{20}+\zeta_{20}^{5}-\zeta_{20}^{7})q^{3}+\cdots\)
770.2.ba.b \(64\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)
770.2.ba.c \(72\) \(6.148\) None \(0\) \(0\) \(-8\) \(0\)

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

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)