Properties

Label 770.2.l
Level $770$
Weight $2$
Character orbit 770.l
Rep. character $\chi_{770}(573,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $80$
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.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
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 304 80 224
Cusp forms 272 80 192
Eisenstein series 32 0 32

Trace form

\( 80q + O(q^{10}) \) \( 80q + 48q^{15} - 80q^{16} - 16q^{18} - 32q^{21} - 48q^{30} + 48q^{35} - 96q^{36} - 24q^{42} + 16q^{43} + 48q^{46} - 16q^{53} + 8q^{56} - 32q^{57} - 32q^{58} + 16q^{60} + 32q^{63} + 16q^{65} - 32q^{67} + 16q^{70} + 16q^{71} - 16q^{72} + 80q^{78} - 112q^{81} + 96q^{85} + 32q^{91} - 16q^{93} + 16q^{95} - 32q^{98} + O(q^{100}) \)

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.l.a \(16\) \(6.148\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{12}q^{2}+\beta _{1}q^{3}-\beta _{8}q^{4}+(\beta _{2}+\beta _{13}+\cdots)q^{5}+\cdots\)
770.2.l.b \(24\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)
770.2.l.c \(40\) \(6.148\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)