Properties

Label 930.4.d
Level $930$
Weight $4$
Character orbit 930.d
Rep. character $\chi_{930}(559,\cdot)$
Character field $\Q$
Dimension $92$
Newform subspaces $5$
Sturm bound $768$
Trace bound $6$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 930.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(768\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(930, [\chi])\).

Total New Old
Modular forms 584 92 492
Cusp forms 568 92 476
Eisenstein series 16 0 16

Trace form

\( 92q - 368q^{4} - 8q^{5} - 828q^{9} + O(q^{10}) \) \( 92q - 368q^{4} - 8q^{5} - 828q^{9} + 64q^{10} - 280q^{11} - 16q^{14} + 48q^{15} + 1472q^{16} - 192q^{19} + 32q^{20} + 200q^{25} - 432q^{26} + 544q^{29} + 224q^{34} + 456q^{35} + 3312q^{36} - 256q^{40} - 72q^{41} + 1120q^{44} + 72q^{45} + 784q^{46} - 4804q^{49} + 1120q^{50} - 264q^{51} - 1648q^{55} + 64q^{56} - 1800q^{59} - 192q^{60} - 992q^{61} - 5888q^{64} + 1168q^{65} + 1056q^{66} + 1200q^{69} + 192q^{70} - 1424q^{71} - 2032q^{74} - 528q^{75} + 768q^{76} - 16q^{79} - 128q^{80} + 7452q^{81} - 3240q^{85} - 352q^{86} - 1848q^{89} - 576q^{90} - 496q^{91} - 2192q^{94} + 1008q^{95} + 2520q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(930, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
930.4.d.a \(2\) \(54.872\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(20\) \(0\) \(q+2iq^{2}+3iq^{3}-4q^{4}+(10+5i)q^{5}+\cdots\)
930.4.d.b \(20\) \(54.872\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q+2\beta _{3}q^{2}+3\beta _{3}q^{3}-4q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
930.4.d.c \(20\) \(54.872\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q+2\beta _{8}q^{2}-3\beta _{8}q^{3}-4q^{4}-\beta _{16}q^{5}+\cdots\)
930.4.d.d \(24\) \(54.872\) None \(0\) \(0\) \(-22\) \(0\)
930.4.d.e \(26\) \(54.872\) None \(0\) \(0\) \(-2\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(930, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(310, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)