Properties

Label 1140.2.u
Level $1140$
Weight $2$
Character orbit 1140.u
Rep. character $\chi_{1140}(77,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $2$
Sturm bound $480$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1140 = 2^{2} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1140.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(480\)
Trace bound: \(7\)

Dimensions

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

Total New Old
Modular forms 504 72 432
Cusp forms 456 72 384
Eisenstein series 48 0 48

Trace form

\( 72q - 4q^{3} + 8q^{7} + O(q^{10}) \) \( 72q - 4q^{3} + 8q^{7} + 16q^{13} + 8q^{15} + 8q^{21} - 24q^{25} - 16q^{27} - 16q^{31} - 16q^{33} + 40q^{37} + 16q^{43} - 24q^{51} + 32q^{55} + 32q^{61} - 8q^{63} + 8q^{67} - 24q^{73} - 32q^{75} + 40q^{81} - 72q^{85} - 32q^{91} + 40q^{93} - 56q^{97} + O(q^{100}) \)

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.u.a \(36\) \(9.103\) None \(0\) \(-2\) \(0\) \(-4\)
1140.2.u.b \(36\) \(9.103\) None \(0\) \(-2\) \(0\) \(12\)

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

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