Properties

Label 230.3.f
Level $230$
Weight $3$
Character orbit 230.f
Rep. character $\chi_{230}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $44$
Newform subspaces $2$
Sturm bound $108$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(108\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(230, [\chi])\).

Total New Old
Modular forms 152 44 108
Cusp forms 136 44 92
Eisenstein series 16 0 16

Trace form

\( 44q + 4q^{2} + 8q^{5} + 16q^{7} - 8q^{8} + O(q^{10}) \) \( 44q + 4q^{2} + 8q^{5} + 16q^{7} - 8q^{8} + 20q^{10} + 48q^{11} - 28q^{13} - 72q^{15} - 176q^{16} - 84q^{17} + 60q^{18} + 8q^{20} - 16q^{21} - 64q^{22} - 12q^{25} - 40q^{26} + 216q^{27} - 32q^{28} + 96q^{30} - 200q^{31} - 16q^{32} - 8q^{33} + 48q^{35} + 232q^{36} - 28q^{37} + 144q^{38} + 40q^{40} + 104q^{41} - 32q^{42} - 236q^{45} + 64q^{47} - 132q^{50} + 240q^{51} - 56q^{52} - 436q^{53} + 248q^{55} - 384q^{57} - 160q^{58} + 176q^{61} + 224q^{62} + 536q^{63} + 60q^{65} + 384q^{66} + 128q^{67} + 168q^{68} - 128q^{70} - 120q^{71} + 120q^{72} - 220q^{73} + 152q^{75} - 64q^{76} + 200q^{77} - 240q^{78} - 32q^{80} - 524q^{81} + 128q^{82} + 288q^{83} + 212q^{85} - 480q^{86} - 32q^{87} + 128q^{88} - 140q^{90} - 624q^{91} + 448q^{93} + 48q^{95} - 708q^{97} - 380q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(230, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
230.3.f.a \(20\) \(6.267\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-20\) \(0\) \(4\) \(8\) \(q+(-1-\beta _{8})q^{2}+\beta _{1}q^{3}+2\beta _{8}q^{4}+\cdots\)
230.3.f.b \(24\) \(6.267\) None \(24\) \(0\) \(4\) \(8\)

Decomposition of \(S_{3}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(230, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)