Properties

Label 230.2.g
Level $230$
Weight $2$
Character orbit 230.g
Rep. character $\chi_{230}(31,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $80$
Newform subspaces $4$
Sturm bound $72$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 230.g (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 4 \)
Sturm bound: \(72\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 400 80 320
Cusp forms 320 80 240
Eisenstein series 80 0 80

Trace form

\( 80 q - 8 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{9} + O(q^{10}) \) \( 80 q - 8 q^{4} + 2 q^{5} + 4 q^{6} - 4 q^{9} + 2 q^{10} + 12 q^{11} + 8 q^{13} + 8 q^{14} - 8 q^{16} - 20 q^{17} + 16 q^{18} - 32 q^{19} + 2 q^{20} - 84 q^{21} - 40 q^{22} + 24 q^{23} + 4 q^{24} - 8 q^{25} - 16 q^{26} - 84 q^{27} - 4 q^{29} + 8 q^{30} - 16 q^{31} + 72 q^{33} + 24 q^{34} - 14 q^{35} - 4 q^{36} + 28 q^{37} + 28 q^{38} + 28 q^{39} + 2 q^{40} + 24 q^{41} + 64 q^{42} - 68 q^{43} + 12 q^{44} - 40 q^{45} + 24 q^{46} + 72 q^{47} - 22 q^{49} + 16 q^{51} + 8 q^{52} + 32 q^{53} + 42 q^{54} - 20 q^{55} - 14 q^{56} - 4 q^{57} - 32 q^{58} - 22 q^{59} - 36 q^{61} - 100 q^{62} - 100 q^{63} - 8 q^{64} + 20 q^{65} - 32 q^{66} - 44 q^{67} - 64 q^{68} + 96 q^{69} + 12 q^{70} + 84 q^{71} - 72 q^{72} - 16 q^{73} - 44 q^{74} + 12 q^{76} - 116 q^{77} - 92 q^{78} - 76 q^{79} + 2 q^{80} - 56 q^{82} - 100 q^{83} + 26 q^{84} + 4 q^{85} - 2 q^{86} - 28 q^{87} + 4 q^{88} + 28 q^{89} + 26 q^{90} + 96 q^{91} + 24 q^{92} + 88 q^{93} + 40 q^{94} + 32 q^{95} + 4 q^{96} + 44 q^{97} + 32 q^{98} + 16 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
230.2.g.a \(10\) \(1.837\) \(\Q(\zeta_{22})\) None \(-1\) \(3\) \(-1\) \(-15\) \(q+\zeta_{22}^{4}q^{2}+(1-\zeta_{22}+\zeta_{22}^{2}+\zeta_{22}^{4}+\cdots)q^{3}+\cdots\)
230.2.g.b \(20\) \(1.837\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(-3\) \(-2\) \(19\) \(q+\beta _{6}q^{2}+(\beta _{1}-\beta _{2}+\beta _{5}-\beta _{13}+\beta _{18}+\cdots)q^{3}+\cdots\)
230.2.g.c \(20\) \(1.837\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(1\) \(2\) \(-12\) \(q+\beta _{3}q^{2}+(\beta _{5}+\beta _{18})q^{3}+\beta _{12}q^{4}+\cdots\)
230.2.g.d \(30\) \(1.837\) None \(-3\) \(-1\) \(3\) \(8\)

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

\( S_{2}^{\mathrm{old}}(230, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)