Properties

Label 930.2.o
Level $930$
Weight $2$
Character orbit 930.o
Rep. character $\chi_{930}(161,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $5$
Sturm bound $384$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(384\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 400 88 312
Cusp forms 368 88 280
Eisenstein series 32 0 32

Trace form

\( 88q - 88q^{4} - 8q^{7} + O(q^{10}) \) \( 88q - 88q^{4} - 8q^{7} + 88q^{16} - 16q^{18} - 16q^{19} + 60q^{21} + 44q^{25} + 8q^{28} + 24q^{31} - 8q^{33} + 12q^{34} - 16q^{39} + 24q^{42} - 8q^{45} - 60q^{49} + 16q^{51} + 12q^{55} - 12q^{57} + 112q^{63} - 88q^{64} - 32q^{66} + 56q^{67} - 4q^{69} + 16q^{72} + 120q^{73} + 16q^{76} - 48q^{78} - 12q^{79} - 48q^{81} - 8q^{82} - 60q^{84} + 8q^{87} - 8q^{90} + 32q^{93} - 24q^{94} - 96q^{97} - 108q^{99} + O(q^{100}) \)

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.o.a \(4\) \(7.426\) \(\Q(\zeta_{12})\) None \(0\) \(-6\) \(0\) \(8\) \(q+\zeta_{12}^{3}q^{2}+(-1-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
930.2.o.b \(4\) \(7.426\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}^{3}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
930.2.o.c \(4\) \(7.426\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) \(q+\zeta_{12}^{3}q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}-q^{4}+\cdots\)
930.2.o.d \(36\) \(7.426\) None \(0\) \(0\) \(0\) \(-8\)
930.2.o.e \(40\) \(7.426\) None \(0\) \(6\) \(0\) \(-12\)

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

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