Properties

Label 770.2.c
Level $770$
Weight $2$
Character orbit 770.c
Rep. character $\chi_{770}(309,\cdot)$
Character field $\Q$
Dimension $28$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(288\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(13\), \(17\)

Dimensions

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

Total New Old
Modular forms 152 28 124
Cusp forms 136 28 108
Eisenstein series 16 0 16

Trace form

\( 28q - 28q^{4} - 4q^{5} - 12q^{9} + O(q^{10}) \) \( 28q - 28q^{4} - 4q^{5} - 12q^{9} - 8q^{10} - 4q^{11} + 8q^{14} - 8q^{15} + 28q^{16} + 4q^{20} - 4q^{25} + 16q^{26} - 8q^{30} - 24q^{31} - 8q^{35} + 12q^{36} - 16q^{39} + 8q^{40} + 48q^{41} + 4q^{44} + 44q^{45} - 28q^{49} - 8q^{50} - 48q^{51} + 12q^{55} - 8q^{56} - 40q^{59} + 8q^{60} + 16q^{61} - 28q^{64} + 40q^{65} - 64q^{69} + 64q^{71} - 24q^{74} + 8q^{75} + 56q^{79} - 4q^{80} + 28q^{81} - 16q^{85} - 32q^{86} - 24q^{89} + 64q^{90} - 8q^{91} + 32q^{95} - 28q^{99} + O(q^{100}) \)

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.c.a \(2\) \(6.148\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q-iq^{2}-q^{4}+(-2+i)q^{5}-iq^{7}+\cdots\)
770.2.c.b \(2\) \(6.148\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q-iq^{2}-q^{4}+(1-2i)q^{5}-iq^{7}+iq^{8}+\cdots\)
770.2.c.c \(2\) \(6.148\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}-q^{4}+(2-i)q^{5}+iq^{7}-iq^{8}+\cdots\)
770.2.c.d \(4\) \(6.148\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) \(q-\beta _{1}q^{2}+\beta _{2}q^{3}-q^{4}+(-1-2\beta _{1}+\cdots)q^{5}+\cdots\)
770.2.c.e \(8\) \(6.148\) 8.0.1698758656.6 None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{5}q^{2}+\beta _{4}q^{3}-q^{4}-\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
770.2.c.f \(10\) \(6.148\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(2\) \(0\) \(q+\beta _{4}q^{2}+\beta _{7}q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{1}q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)