Properties

Label 930.2.h
Level $930$
Weight $2$
Character orbit 930.h
Rep. character $\chi_{930}(371,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $4$
Sturm bound $384$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 93 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 200 40 160
Cusp forms 184 40 144
Eisenstein series 16 0 16

Trace form

\( 40q - 40q^{4} - 24q^{7} + O(q^{10}) \) \( 40q - 40q^{4} - 24q^{7} + 40q^{16} + 16q^{18} + 24q^{19} - 40q^{25} + 24q^{28} + 16q^{31} + 8q^{33} - 8q^{39} + 8q^{45} - 16q^{51} + 8q^{63} - 40q^{64} - 16q^{66} + 72q^{67} + 16q^{69} - 16q^{72} - 24q^{76} + 24q^{78} - 24q^{81} - 16q^{82} - 32q^{87} - 16q^{90} + 16q^{93} + 16q^{97} + O(q^{100}) \)

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.h.a \(4\) \(7.426\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(-16\) \(q+\beta _{2}q^{2}-\beta _{3}q^{3}-q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
930.2.h.b \(4\) \(7.426\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-q^{4}-\zeta_{12}q^{5}+\cdots\)
930.2.h.c \(16\) \(7.426\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-20\) \(q+\beta _{3}q^{2}-\beta _{5}q^{3}-q^{4}+\beta _{3}q^{5}+\beta _{1}q^{6}+\cdots\)
930.2.h.d \(16\) \(7.426\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{6}q^{2}-\beta _{12}q^{3}-q^{4}+\beta _{6}q^{5}+\beta _{5}q^{6}+\cdots\)

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

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