Properties

Label 770.2.m
Level $770$
Weight $2$
Character orbit 770.m
Rep. character $\chi_{770}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $6$
Sturm bound $288$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(17\)

Dimensions

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

Total New Old
Modular forms 304 72 232
Cusp forms 272 72 200
Eisenstein series 32 0 32

Trace form

\( 72 q - 8 q^{3} + O(q^{10}) \) \( 72 q - 8 q^{3} + 8 q^{11} + 8 q^{12} - 8 q^{15} - 72 q^{16} - 8 q^{20} - 8 q^{22} + 8 q^{23} + 40 q^{25} + 16 q^{27} + 32 q^{31} - 40 q^{33} - 88 q^{36} + 8 q^{37} + 48 q^{38} - 24 q^{45} + 24 q^{47} + 8 q^{48} - 40 q^{53} - 40 q^{60} - 32 q^{66} + 40 q^{67} - 16 q^{70} - 96 q^{71} + 72 q^{75} - 16 q^{77} + 32 q^{78} - 120 q^{81} + 32 q^{82} + 128 q^{86} - 8 q^{88} + 48 q^{91} - 8 q^{92} + 32 q^{93} + 88 q^{97} + O(q^{100}) \)

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.m.a \(4\) \(6.148\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-8\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(-2-\zeta_{8}^{2})q^{5}+\cdots\)
770.2.m.b \(4\) \(6.148\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+(1+2\zeta_{8}^{2})q^{5}+\cdots\)
770.2.m.c \(4\) \(6.148\) \(\Q(\zeta_{8})\) None \(0\) \(8\) \(-4\) \(0\) \(q+\zeta_{8}q^{2}+(2+2\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
770.2.m.d \(8\) \(6.148\) 8.0.40960000.1 None \(0\) \(-4\) \(16\) \(0\) \(q-\beta _{7}q^{2}+\beta _{5}q^{3}-\beta _{2}q^{4}+(2-\beta _{2}+\cdots)q^{5}+\cdots\)
770.2.m.e \(16\) \(6.148\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-8\) \(-8\) \(0\) \(q-\beta _{10}q^{2}+(-1-\beta _{3}+\beta _{7}-\beta _{15})q^{3}+\cdots\)
770.2.m.f \(36\) \(6.148\) None \(0\) \(-4\) \(0\) \(0\)

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

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