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Properties

Label 230.5.f
Level $230$
Weight $5$
Character orbit 230.f
Rep. character $\chi_{230}(47,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $2$
Sturm bound $180$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 5 \)
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: \(180\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(230, [\chi])\).

Total New Old
Modular forms 296 88 208
Cusp forms 280 88 192
Eisenstein series 16 0 16

Trace form

\( 88 q + 48 q^{5} - 160 q^{7} + O(q^{10}) \) \( 88 q + 48 q^{5} - 160 q^{7} - 320 q^{10} - 624 q^{11} + 520 q^{13} + 408 q^{15} - 5632 q^{16} + 1200 q^{17} - 192 q^{20} - 3952 q^{21} - 1280 q^{22} + 168 q^{25} + 1920 q^{26} - 3240 q^{27} + 1280 q^{28} - 4224 q^{30} + 1640 q^{31} + 760 q^{33} + 8928 q^{35} + 21184 q^{36} + 4960 q^{37} - 5760 q^{38} - 2560 q^{40} - 1032 q^{41} + 4480 q^{42} - 10856 q^{45} + 1200 q^{47} + 12288 q^{50} + 18480 q^{51} + 4160 q^{52} + 10440 q^{53} + 10408 q^{55} - 12480 q^{57} - 7040 q^{58} + 14272 q^{61} + 9600 q^{62} - 8920 q^{63} - 13320 q^{65} - 26112 q^{66} - 7040 q^{67} - 9600 q^{68} - 14848 q^{70} + 6840 q^{71} + 33040 q^{73} + 13112 q^{75} + 9472 q^{76} - 18120 q^{77} - 24960 q^{78} - 3072 q^{80} - 120728 q^{81} - 18560 q^{82} - 15840 q^{83} - 25688 q^{85} + 7680 q^{86} - 80 q^{87} + 10240 q^{88} + 7360 q^{90} - 43728 q^{91} + 15040 q^{93} - 6432 q^{95} + 38040 q^{97} + 23040 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(230, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
230.5.f.a 230.f 5.c $44$ $23.775$ None \(-88\) \(0\) \(24\) \(-80\) $\mathrm{SU}(2)[C_{4}]$
230.5.f.b 230.f 5.c $44$ $23.775$ None \(88\) \(0\) \(24\) \(-80\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{5}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(230, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)