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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
230.3.f.a 230.f 5.c $20$ $6.267$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-20\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{8})q^{2}+\beta _{1}q^{3}+2\beta _{8}q^{4}+\cdots\)
230.3.f.b 230.f 5.c $24$ $6.267$ None \(24\) \(0\) \(4\) \(8\) $\mathrm{SU}(2)[C_{4}]$

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

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