Properties

Label 231.2.w
Level $231$
Weight $2$
Character orbit 231.w
Rep. character $\chi_{231}(13,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $64$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 231.w (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(231, [\chi])\).

Total New Old
Modular forms 144 64 80
Cusp forms 112 64 48
Eisenstein series 32 0 32

Trace form

\( 64q + 12q^{4} + 10q^{7} - 20q^{8} + 16q^{9} + O(q^{10}) \) \( 64q + 12q^{4} + 10q^{7} - 20q^{8} + 16q^{9} - 16q^{11} + 12q^{14} - 12q^{15} - 16q^{16} + 10q^{18} - 40q^{22} - 24q^{23} + 44q^{25} - 30q^{28} - 40q^{29} - 40q^{35} - 12q^{36} + 32q^{37} - 2q^{42} + 22q^{44} - 70q^{46} - 50q^{49} - 40q^{51} - 64q^{53} + 80q^{56} + 2q^{58} - 36q^{60} + 10q^{63} + 72q^{64} - 8q^{67} - 26q^{70} + 68q^{71} - 10q^{72} + 80q^{74} + 90q^{77} - 72q^{78} + 40q^{79} - 16q^{81} + 60q^{84} - 40q^{85} - 62q^{86} + 140q^{88} + 54q^{91} + 18q^{92} - 20q^{93} + 20q^{95} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(231, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
231.2.w.a \(64\) \(1.845\) None \(0\) \(0\) \(0\) \(10\)

Decomposition of \(S_{2}^{\mathrm{old}}(231, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(231, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)