Properties

Label 930.2.bg
Level $930$
Weight $2$
Character orbit 930.bg
Rep. character $\chi_{930}(121,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $160$
Newform subspaces $9$
Sturm bound $384$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bg (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 9 \)
Sturm bound: \(384\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 1600 160 1440
Cusp forms 1472 160 1312
Eisenstein series 128 0 128

Trace form

\( 160q - 40q^{4} + 20q^{9} + O(q^{10}) \) \( 160q - 40q^{4} + 20q^{9} - 48q^{11} - 16q^{13} - 48q^{14} - 40q^{16} - 32q^{17} + 16q^{23} - 80q^{25} + 32q^{26} + 64q^{29} + 32q^{30} + 40q^{31} + 48q^{33} + 36q^{34} + 48q^{35} - 80q^{36} - 48q^{37} + 16q^{38} - 40q^{39} + 40q^{41} + 8q^{42} - 8q^{43} - 8q^{44} - 28q^{46} - 16q^{47} + 60q^{49} - 56q^{51} - 16q^{52} + 56q^{53} - 24q^{55} - 8q^{56} - 16q^{57} - 56q^{58} + 40q^{59} - 80q^{61} - 40q^{64} + 4q^{66} + 56q^{67} + 8q^{68} - 56q^{71} + 56q^{73} - 16q^{74} + 96q^{77} - 24q^{78} + 40q^{79} + 20q^{81} + 56q^{82} + 8q^{83} - 40q^{85} - 40q^{86} - 8q^{87} - 40q^{88} - 72q^{89} + 72q^{91} - 64q^{92} + 8q^{93} + 24q^{94} + 112q^{97} + 32q^{98} - 8q^{99} + O(q^{100}) \)

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.bg.a \(8\) \(7.426\) \(\Q(\zeta_{15})\) None \(-2\) \(-1\) \(4\) \(2\) \(q+\zeta_{15}^{3}q^{2}-\zeta_{15}^{7}q^{3}+\zeta_{15}^{6}q^{4}+\cdots\)
930.2.bg.b \(16\) \(7.426\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-4\) \(-2\) \(-8\) \(3\) \(q-\beta _{5}q^{2}+\beta _{10}q^{3}+(-1+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots\)
930.2.bg.c \(16\) \(7.426\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-4\) \(-2\) \(8\) \(11\) \(q+(\beta _{4}+\beta _{7}+\beta _{8}+\beta _{9}-\beta _{10})q^{2}+\beta _{10}q^{3}+\cdots\)
930.2.bg.d \(16\) \(7.426\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-4\) \(2\) \(8\) \(11\) \(q+\beta _{4}q^{2}+(\beta _{5}+\beta _{7})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
930.2.bg.e \(16\) \(7.426\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(-2\) \(8\) \(-5\) \(q+\beta _{9}q^{2}+(-1+\beta _{3}+\beta _{4}-\beta _{6}+\beta _{9}+\cdots)q^{3}+\cdots\)
930.2.bg.f \(16\) \(7.426\) 16.0.\(\cdots\).1 None \(4\) \(2\) \(-8\) \(-13\) \(q+(1-\beta _{11}-\beta _{13}+\beta _{15})q^{2}+(-\beta _{3}+\cdots)q^{3}+\cdots\)
930.2.bg.g \(24\) \(7.426\) None \(-6\) \(3\) \(-12\) \(9\)
930.2.bg.h \(24\) \(7.426\) None \(6\) \(-3\) \(-12\) \(-11\)
930.2.bg.i \(24\) \(7.426\) None \(6\) \(3\) \(12\) \(-7\)

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

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