Properties

Label 4140.2.f
Level $4140$
Weight $2$
Character orbit 4140.f
Rep. character $\chi_{4140}(829,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $4$
Sturm bound $1728$
Trace bound $1$

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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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(1728\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 888 56 832
Cusp forms 840 56 784
Eisenstein series 48 0 48

Trace form

\( 56 q + O(q^{10}) \) \( 56 q - 4 q^{11} + 8 q^{19} - 4 q^{25} + 22 q^{29} - 14 q^{31} + 22 q^{35} - 34 q^{41} - 50 q^{49} - 2 q^{59} - 6 q^{65} + 6 q^{71} - 36 q^{79} - 18 q^{85} + 8 q^{89} + 8 q^{91} + 4 q^{95} + O(q^{100}) \)

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.f.a 4140.f 5.b $6$ $33.058$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{4})q^{5}-\beta _{3}q^{7}+\beta _{1}q^{11}+(\beta _{3}+\cdots)q^{13}+\cdots\)
4140.2.f.b 4140.f 5.b $12$ $33.058$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{5}+(\beta _{1}+\beta _{6}-\beta _{10})q^{7}+(-1+\cdots)q^{11}+\cdots\)
4140.2.f.c 4140.f 5.b $14$ $33.058$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{5}+\beta _{13}q^{7}+(-1+\beta _{2}-\beta _{4}+\cdots)q^{11}+\cdots\)
4140.2.f.d 4140.f 5.b $24$ $33.058$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(4140, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(460, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2070, [\chi])\)\(^{\oplus 2}\)