Properties

Label 231.2.e
Level $231$
Weight $2$
Character orbit 231.e
Rep. character $\chi_{231}(188,\cdot)$
Character field $\Q$
Dimension $28$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
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 36 28 8
Cusp forms 28 28 0
Eisenstein series 8 0 8

Trace form

\( 28q - 32q^{4} - 8q^{7} - 8q^{9} + O(q^{10}) \) \( 28q - 32q^{4} - 8q^{7} - 8q^{9} - 20q^{15} + 40q^{16} - 12q^{18} - 10q^{21} + 36q^{25} + 12q^{28} - 4q^{30} + 24q^{36} - 24q^{37} + 16q^{39} - 40q^{43} - 16q^{46} + 4q^{49} - 8q^{51} - 4q^{57} - 44q^{58} + 52q^{60} + 6q^{63} - 68q^{64} + 40q^{67} + 20q^{70} + 24q^{72} - 28q^{78} + 56q^{79} + 32q^{81} + 100q^{84} - 8q^{85} + 12q^{88} + 8q^{91} - 36q^{93} + O(q^{100}) \)

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.e.a \(28\) \(1.845\) None \(0\) \(0\) \(0\) \(-8\)