Properties

Label 230.2.b
Level $230$
Weight $2$
Character orbit 230.b
Rep. character $\chi_{230}(139,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
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: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(230, [\chi])\).

Total New Old
Modular forms 40 12 28
Cusp forms 32 12 20
Eisenstein series 8 0 8

Trace form

\( 12 q - 12 q^{4} + 4 q^{6} - 8 q^{9} - 8 q^{11} - 16 q^{15} + 12 q^{16} + 16 q^{19} - 4 q^{24} + 8 q^{25} + 4 q^{26} + 8 q^{29} - 12 q^{31} - 16 q^{35} + 8 q^{36} - 8 q^{39} + 28 q^{41} + 8 q^{44} - 16 q^{45}+ \cdots + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(230, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
230.2.b.a 230.b 5.b $4$ $1.837$ \(\Q(i, \sqrt{5})\) None 230.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{1}q^{3}-q^{4}+(1+2\beta _{2})q^{5}+\cdots\)
230.2.b.b 230.b 5.b $8$ $1.837$ 8.0.\(\cdots\).3 None 230.2.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{5})q^{3}-q^{4}+(\beta _{1}-\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(230, [\chi])\) into lower level spaces

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