Properties

Label 930.2.d
Level $930$
Weight $2$
Character orbit 930.d
Rep. character $\chi_{930}(559,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $9$
Sturm bound $384$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(384\)
Trace bound: \(11\)
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 200 28 172
Cusp forms 184 28 156
Eisenstein series 16 0 16

Trace form

\( 28 q - 28 q^{4} + 8 q^{5} - 28 q^{9} + O(q^{10}) \) \( 28 q - 28 q^{4} + 8 q^{5} - 28 q^{9} - 8 q^{11} - 8 q^{14} - 8 q^{15} + 28 q^{16} + 16 q^{19} - 8 q^{20} + 24 q^{26} - 16 q^{29} - 16 q^{34} + 28 q^{36} + 24 q^{41} + 8 q^{44} - 8 q^{45} + 8 q^{46} - 20 q^{49} - 16 q^{50} + 8 q^{51} - 24 q^{55} + 8 q^{56} + 24 q^{59} + 8 q^{60} - 28 q^{64} - 40 q^{65} - 16 q^{66} + 16 q^{69} + 32 q^{71} - 8 q^{74} + 32 q^{75} - 16 q^{76} - 48 q^{79} + 8 q^{80} + 28 q^{81} - 24 q^{85} + 16 q^{86} - 72 q^{89} + 32 q^{91} + 56 q^{94} - 24 q^{95} + 8 q^{99} + O(q^{100}) \)

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.d.a 930.d 5.b $2$ $7.426$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+(-1+2i)q^{5}+\cdots\)
930.2.d.b 930.d 5.b $2$ $7.426$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
930.2.d.c 930.d 5.b $2$ $7.426$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+(1+2i)q^{5}+q^{6}+\cdots\)
930.2.d.d 930.d 5.b $2$ $7.426$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-iq^{3}-q^{4}+(2+i)q^{5}-q^{6}+\cdots\)
930.2.d.e 930.d 5.b $2$ $7.426$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+(2+i)q^{5}+q^{6}+\cdots\)
930.2.d.f 930.d 5.b $2$ $7.426$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}+q^{6}+\cdots\)
930.2.d.g 930.d 5.b $4$ $7.426$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{2}+\zeta_{8}q^{3}-q^{4}+(2+\zeta_{8})q^{5}+\cdots\)
930.2.d.h 930.d 5.b $6$ $7.426$ 6.0.3534400.1 None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{5}q^{3}-q^{4}+(-1+\beta _{4}+\cdots)q^{5}+\cdots\)
930.2.d.i 930.d 5.b $6$ $7.426$ 6.0.11669056.1 None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

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

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