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Properties

Label 230.6.b
Level $230$
Weight $6$
Character orbit 230.b
Rep. character $\chi_{230}(139,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $2$
Sturm bound $216$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 230.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(216\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(230, [\chi])\).

Total New Old
Modular forms 184 56 128
Cusp forms 176 56 120
Eisenstein series 8 0 8

Trace form

\( 56 q - 896 q^{4} - 60 q^{5} + 144 q^{6} - 4420 q^{9} + O(q^{10}) \) \( 56 q - 896 q^{4} - 60 q^{5} + 144 q^{6} - 4420 q^{9} + 160 q^{10} + 760 q^{11} - 1776 q^{15} + 14336 q^{16} + 4880 q^{19} + 960 q^{20} - 9536 q^{21} - 2304 q^{24} + 1748 q^{25} + 10064 q^{26} - 11464 q^{29} + 10080 q^{30} + 31588 q^{31} - 21760 q^{34} + 17504 q^{35} + 70720 q^{36} + 24120 q^{39} - 2560 q^{40} + 35932 q^{41} - 12160 q^{44} - 93436 q^{45} + 8464 q^{46} - 158972 q^{49} + 29968 q^{50} - 154536 q^{51} + 46080 q^{54} + 27192 q^{55} - 85576 q^{59} + 28416 q^{60} - 55848 q^{61} - 229376 q^{64} - 38376 q^{65} - 72928 q^{66} - 38088 q^{69} - 105200 q^{70} + 161724 q^{71} + 142272 q^{74} + 17168 q^{75} - 78080 q^{76} + 418128 q^{79} - 15360 q^{80} + 242184 q^{81} + 152576 q^{84} + 188496 q^{85} + 205600 q^{86} + 116104 q^{89} + 21056 q^{90} - 120736 q^{91} + 8288 q^{94} + 369728 q^{95} + 36864 q^{96} - 54784 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(230, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
230.6.b.a 230.b 5.b $26$ $36.888$ None \(0\) \(0\) \(-30\) \(0\) $\mathrm{SU}(2)[C_{2}]$
230.6.b.b 230.b 5.b $30$ $36.888$ None \(0\) \(0\) \(-30\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{6}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(230, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 2}\)