Properties

Label 930.2.j
Level $930$
Weight $2$
Character orbit 930.j
Rep. character $\chi_{930}(497,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $120$
Newform subspaces $8$
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.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 8 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\)

Dimensions

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

Total New Old
Modular forms 400 120 280
Cusp forms 368 120 248
Eisenstein series 32 0 32

Trace form

\( 120 q + 8 q^{6} + O(q^{10}) \) \( 120 q + 8 q^{6} - 24 q^{15} - 120 q^{16} - 16 q^{18} - 16 q^{21} + 24 q^{27} + 40 q^{33} + 8 q^{36} + 16 q^{37} - 16 q^{40} - 32 q^{42} - 48 q^{43} + 56 q^{45} - 48 q^{46} + 32 q^{51} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 16 q^{60} + 80 q^{61} - 48 q^{63} - 48 q^{66} - 16 q^{67} - 32 q^{70} + 16 q^{72} + 80 q^{73} - 64 q^{75} + 16 q^{78} + 40 q^{81} + 32 q^{82} - 80 q^{85} + 40 q^{87} - 32 q^{90} - 8 q^{96} - 32 q^{97} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
930.2.j.a 930.j 15.e $4$ $7.426$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{3}q^{2}+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
930.2.j.b 930.j 15.e $4$ $7.426$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}-\zeta_{8}^{2})q^{3}-\zeta_{8}^{2}q^{4}+\cdots\)
930.2.j.c 930.j 15.e $8$ $7.426$ 8.0.1698758656.6 None \(0\) \(-8\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}+(-1-\beta _{1}-\beta _{7})q^{3}-\beta _{7}q^{4}+\cdots\)
930.2.j.d 930.j 15.e $8$ $7.426$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{24}q^{2}+\zeta_{24}^{2}q^{3}+\zeta_{24}^{3}q^{4}+(\zeta_{24}+\cdots)q^{5}+\cdots\)
930.2.j.e 930.j 15.e $8$ $7.426$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\zeta_{24}+\zeta_{24}^{5})q^{2}+(\zeta_{24}+\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
930.2.j.f 930.j 15.e $8$ $7.426$ 8.0.1698758656.6 None \(0\) \(8\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{7})q^{3}-\beta _{7}q^{4}+\cdots\)
930.2.j.g 930.j 15.e $40$ $7.426$ None \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
930.2.j.h 930.j 15.e $40$ $7.426$ None \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)