↑

Properties

Label 930.2.z
Level $930$
Weight $2$
Character orbit 930.z
Rep. character $\chi_{930}(109,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $128$
Newform subspaces $4$
Sturm bound $384$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 4 \)
Sturm bound: \(384\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 800 128 672
Cusp forms 736 128 608
Eisenstein series 64 0 64

Trace form

\( 128 q + 32 q^{4} + 16 q^{6} + 32 q^{9} + O(q^{10}) \) \( 128 q + 32 q^{4} + 16 q^{6} + 32 q^{9} + 4 q^{10} + 4 q^{15} - 32 q^{16} - 16 q^{19} - 32 q^{21} + 4 q^{24} - 12 q^{25} + 56 q^{29} + 8 q^{30} + 16 q^{31} + 28 q^{34} - 8 q^{35} + 128 q^{36} + 16 q^{39} + 6 q^{40} - 72 q^{41} - 44 q^{46} + 28 q^{49} - 40 q^{50} + 4 q^{54} - 64 q^{59} - 4 q^{60} + 112 q^{61} + 32 q^{64} + 44 q^{65} - 12 q^{66} + 56 q^{70} - 40 q^{71} + 24 q^{75} - 24 q^{76} + 108 q^{79} - 32 q^{81} - 8 q^{84} - 44 q^{85} + 88 q^{86} - 88 q^{89} - 4 q^{90} - 24 q^{94} + 44 q^{95} - 4 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.z.a 930.z 155.n $8$ $7.426$ \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}+\zeta_{20}^{7})q^{2}+\cdots\)
930.2.z.b 930.z 155.n $16$ $7.426$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{12}q^{2}-\beta _{14}q^{3}-\beta _{15}q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
930.2.z.c 930.z 155.n $32$ $7.426$ None \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{10}]$
930.2.z.d 930.z 155.n $72$ $7.426$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{10}]$

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

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