Properties

Label 930.2.i
Level $930$
Weight $2$
Character orbit 930.i
Rep. character $\chi_{930}(211,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $40$
Newform subspaces $14$
Sturm bound $384$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 14 \)
Sturm bound: \(384\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(930, [\chi])\).

Total New Old
Modular forms 400 40 360
Cusp forms 368 40 328
Eisenstein series 32 0 32

Trace form

\( 40q + 40q^{4} - 20q^{9} + O(q^{10}) \) \( 40q + 40q^{4} - 20q^{9} + 8q^{11} - 24q^{13} + 8q^{14} + 40q^{16} - 8q^{17} + 64q^{23} - 20q^{25} + 8q^{26} + 16q^{29} + 8q^{30} + 32q^{33} + 4q^{34} + 32q^{35} - 20q^{36} + 8q^{37} + 24q^{38} - 8q^{42} - 32q^{43} + 8q^{44} + 8q^{46} + 16q^{47} - 20q^{49} + 16q^{51} - 24q^{52} + 24q^{53} + 4q^{55} + 8q^{56} - 24q^{57} + 16q^{58} + 40q^{64} - 24q^{66} - 16q^{67} - 8q^{68} + 16q^{71} - 16q^{73} - 24q^{74} - 16q^{77} - 16q^{78} + 20q^{79} - 20q^{81} + 24q^{82} - 8q^{83} + 8q^{87} + 32q^{89} + 48q^{91} + 64q^{92} - 8q^{93} + 56q^{94} + 48q^{97} - 32q^{98} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(930, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
930.2.i.a \(2\) \(7.426\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-1\) \(1\) \(1\) \(q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+\cdots\)
930.2.i.b \(2\) \(7.426\) \(\Q(\sqrt{-3}) \) None \(-2\) \(1\) \(1\) \(-3\) \(q-q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{6}+\cdots\)
930.2.i.c \(2\) \(7.426\) \(\Q(\sqrt{-3}) \) None \(-2\) \(1\) \(1\) \(3\) \(q-q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{6}+\cdots\)
930.2.i.d \(2\) \(7.426\) \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(-1\) \(-5\) \(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots\)
930.2.i.e \(2\) \(7.426\) \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(-1\) \(0\) \(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots\)
930.2.i.f \(2\) \(7.426\) \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(-1\) \(1\) \(q+q^{2}+(-1+\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+\cdots\)
930.2.i.g \(2\) \(7.426\) \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(1\) \(-4\) \(q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots\)
930.2.i.h \(2\) \(7.426\) \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(1\) \(3\) \(q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots\)
930.2.i.i \(2\) \(7.426\) \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(1\) \(3\) \(q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}+\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots\)
930.2.i.j \(4\) \(7.426\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(-4\) \(-2\) \(-2\) \(-2\) \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+\cdots\)
930.2.i.k \(4\) \(7.426\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-4\) \(-2\) \(2\) \(1\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(1-\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
930.2.i.l \(4\) \(7.426\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(4\) \(-2\) \(2\) \(4\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{1})q^{5}+\beta _{1}q^{6}+\cdots\)
930.2.i.m \(4\) \(7.426\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(4\) \(2\) \(-2\) \(2\) \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+\beta _{2}q^{5}+(1+\cdots)q^{6}+\cdots\)
930.2.i.n \(6\) \(7.426\) 6.0.3636603.4 None \(-6\) \(3\) \(-3\) \(-4\) \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{1})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(930, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(31, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(62, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)