Properties

Label 1140.2.f
Level $1140$
Weight $2$
Character orbit 1140.f
Rep. character $\chi_{1140}(229,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $480$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1140.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(480\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1140, [\chi])\).

Total New Old
Modular forms 252 16 236
Cusp forms 228 16 212
Eisenstein series 24 0 24

Trace form

\( 16q - 2q^{5} - 16q^{9} + O(q^{10}) \) \( 16q - 2q^{5} - 16q^{9} + 4q^{11} + 4q^{15} + 4q^{19} - 6q^{25} - 8q^{29} - 8q^{31} - 18q^{35} - 8q^{39} + 32q^{41} + 2q^{45} + 20q^{49} - 8q^{51} - 14q^{55} + 16q^{59} - 20q^{61} - 4q^{65} + 8q^{69} - 16q^{71} + 24q^{75} + 16q^{81} - 14q^{85} - 24q^{89} + 8q^{91} - 2q^{95} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1140, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1140.2.f.a \(6\) \(9.103\) 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}+(-\beta _{1}+\beta _{4})q^{5}-\beta _{5}q^{7}+\cdots\)
1140.2.f.b \(10\) \(9.103\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{4}q^{3}+\beta _{9}q^{5}+\beta _{6}q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(570, [\chi])\)\(^{\oplus 2}\)