Properties

Label 770.2.i
Level $770$
Weight $2$
Character orbit 770.i
Rep. character $\chi_{770}(221,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $13$
Sturm bound $288$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 770.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 13 \)
Sturm bound: \(288\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(13\)

Dimensions

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

Total New Old
Modular forms 304 48 256
Cusp forms 272 48 224
Eisenstein series 32 0 32

Trace form

\( 48q - 24q^{4} - 4q^{5} - 8q^{6} + 16q^{7} - 12q^{9} + O(q^{10}) \) \( 48q - 24q^{4} - 4q^{5} - 8q^{6} + 16q^{7} - 12q^{9} - 16q^{13} + 8q^{14} - 24q^{16} - 16q^{19} + 8q^{20} + 4q^{21} + 4q^{24} - 24q^{25} - 8q^{28} - 24q^{29} + 4q^{30} + 16q^{31} - 8q^{33} - 16q^{34} - 8q^{35} + 24q^{36} - 16q^{37} - 24q^{38} - 8q^{39} + 24q^{41} - 8q^{42} + 80q^{43} - 8q^{45} - 4q^{46} + 32q^{47} + 4q^{49} - 48q^{51} + 8q^{52} - 24q^{53} + 28q^{54} - 4q^{56} + 128q^{57} - 8q^{58} - 8q^{59} + 44q^{61} - 48q^{63} + 48q^{64} - 8q^{67} - 8q^{69} - 12q^{70} + 64q^{71} - 64q^{73} + 16q^{74} + 32q^{76} - 8q^{77} + 64q^{78} - 32q^{79} - 4q^{80} - 24q^{81} - 32q^{82} - 32q^{83} - 8q^{84} - 16q^{85} - 4q^{86} - 48q^{87} + 28q^{89} - 24q^{91} - 80q^{93} - 24q^{94} + 8q^{95} + 4q^{96} + 16q^{98} + O(q^{100}) \)

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.i.a \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(1\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.b \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.c \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(-1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.d \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-1\) \(1\) \(q+\zeta_{6}q^{2}+(-3+3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.e \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.f \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.g \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.h \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(1\) \(5\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.i \(2\) \(6.148\) \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-1\) \(5\) \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
770.2.i.j \(6\) \(6.148\) \(\Q(\zeta_{18})\) None \(3\) \(0\) \(-3\) \(0\) \(q+(1-\zeta_{18}^{3})q^{2}+(-\zeta_{18}+\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots\)
770.2.i.k \(6\) \(6.148\) 6.0.64827.1 None \(3\) \(0\) \(3\) \(0\) \(q+(1-\beta _{5})q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
770.2.i.l \(8\) \(6.148\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(1\) \(4\) \(3\) \(q+(-1-\beta _{5})q^{2}+\beta _{1}q^{3}+\beta _{5}q^{4}+(1+\cdots)q^{5}+\cdots\)
770.2.i.m \(10\) \(6.148\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-5\) \(0\) \(-5\) \(0\) \(q+(-1+\beta _{6})q^{2}+(\beta _{1}-\beta _{2})q^{3}-\beta _{6}q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(770, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)