Properties

Label 930.2.n
Level $930$
Weight $2$
Character orbit 930.n
Rep. character $\chi_{930}(481,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $96$
Newform subspaces $8$
Sturm bound $384$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.n (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 8 \)
Sturm bound: \(384\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 800 96 704
Cusp forms 736 96 640
Eisenstein series 64 0 64

Trace form

\( 96q - 4q^{3} - 24q^{4} - 8q^{7} - 24q^{9} + O(q^{10}) \) \( 96q - 4q^{3} - 24q^{4} - 8q^{7} - 24q^{9} + 24q^{11} - 4q^{12} + 8q^{13} + 24q^{14} - 24q^{16} + 8q^{17} - 8q^{19} + 12q^{21} - 24q^{22} + 8q^{23} + 96q^{25} + 64q^{26} - 4q^{27} + 12q^{28} + 8q^{29} + 16q^{30} + 40q^{31} + 24q^{33} + 12q^{34} + 24q^{35} + 96q^{36} - 8q^{37} + 32q^{38} + 28q^{39} + 32q^{41} - 8q^{42} - 4q^{43} - 16q^{44} - 20q^{46} - 32q^{47} - 4q^{48} + 8q^{51} + 8q^{52} - 8q^{53} + 12q^{55} - 16q^{56} + 8q^{57} - 16q^{58} + 32q^{59} + 24q^{61} - 24q^{62} - 8q^{63} - 24q^{64} - 4q^{66} + 8q^{67} - 32q^{68} + 8q^{71} + 8q^{73} - 8q^{74} - 4q^{75} + 12q^{76} - 24q^{77} + 24q^{78} + 32q^{79} - 24q^{81} - 8q^{82} - 32q^{83} - 8q^{84} + 16q^{85} - 8q^{86} - 16q^{87} + 16q^{88} - 24q^{89} + 76q^{91} - 32q^{92} - 36q^{93} - 24q^{94} + 20q^{97} - 32q^{98} - 16q^{99} + O(q^{100}) \)

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.n.a \(8\) \(7.426\) 8.0.13140625.1 None \(-2\) \(2\) \(8\) \(9\) \(q-\beta _{3}q^{2}-\beta _{7}q^{3}+\beta _{4}q^{4}+q^{5}-q^{6}+\cdots\)
930.2.n.b \(8\) \(7.426\) 8.0.1816890625.5 None \(2\) \(2\) \(-8\) \(-7\) \(q-\beta _{2}q^{2}+\beta _{6}q^{3}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
930.2.n.c \(12\) \(7.426\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-3\) \(-3\) \(-12\) \(-1\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+\beta _{8}q^{4}-q^{5}+q^{6}+\cdots\)
930.2.n.d \(12\) \(7.426\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(3\) \(-12\) \(-1\) \(q+(-1-\beta _{3}+\beta _{5}-\beta _{6})q^{2}+\beta _{5}q^{3}+\cdots\)
930.2.n.e \(12\) \(7.426\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(-3\) \(12\) \(-1\) \(q-\beta _{7}q^{2}+\beta _{5}q^{3}+(-1-\beta _{5}-\beta _{7}+\cdots)q^{4}+\cdots\)
930.2.n.f \(12\) \(7.426\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(3\) \(12\) \(-1\) \(q+\beta _{8}q^{2}-\beta _{6}q^{3}+(-1-\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots\)
930.2.n.g \(16\) \(7.426\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(-4\) \(16\) \(1\) \(q+\beta _{6}q^{2}-\beta _{7}q^{3}+(-1-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
930.2.n.h \(16\) \(7.426\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(-4\) \(-16\) \(-7\) \(q+\beta _{7}q^{2}+\beta _{3}q^{3}+(-1-\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)

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

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