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Properties

Label 4140.2.s
Level $4140$
Weight $2$
Character orbit 4140.s
Rep. character $\chi_{4140}(737,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $88$
Newform subspaces $2$
Sturm bound $1728$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 4140 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4140.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(1728\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4140, [\chi])\).

Total New Old
Modular forms 1776 88 1688
Cusp forms 1680 88 1592
Eisenstein series 96 0 96

Trace form

\( 88 q - 16 q^{7} + O(q^{10}) \) \( 88 q - 16 q^{7} - 8 q^{13} + 32 q^{31} - 8 q^{37} + 16 q^{55} - 32 q^{61} - 32 q^{67} - 8 q^{73} - 32 q^{85} - 96 q^{91} + 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(4140, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
4140.2.s.a 4140.s 15.e $44$ $33.058$ None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{4}]$
4140.2.s.b 4140.s 15.e $44$ $33.058$ None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(4140, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2070, [\chi])\)\(^{\oplus 2}\)