Properties

Label 2070.3.c
Level $2070$
Weight $3$
Character orbit 2070.c
Rep. character $\chi_{2070}(91,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $3$
Sturm bound $1296$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2070.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 23 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(1296\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2070, [\chi])\).

Total New Old
Modular forms 880 80 800
Cusp forms 848 80 768
Eisenstein series 32 0 32

Trace form

\( 80 q + 160 q^{4} + O(q^{10}) \) \( 80 q + 160 q^{4} + 24 q^{13} + 320 q^{16} + 76 q^{23} - 400 q^{25} - 96 q^{26} - 12 q^{29} - 148 q^{31} + 60 q^{35} + 84 q^{41} + 4 q^{46} - 272 q^{47} - 764 q^{49} + 48 q^{52} + 32 q^{58} - 324 q^{59} - 224 q^{62} + 640 q^{64} - 120 q^{70} - 340 q^{71} + 304 q^{73} + 696 q^{77} + 64 q^{82} + 60 q^{85} + 152 q^{92} - 24 q^{94} + 320 q^{95} - 320 q^{98} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(2070, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2070.3.c.a 2070.c 23.b $16$ $56.403$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+2q^{4}-\beta _{2}q^{5}+(\beta _{1}+\beta _{7}+\cdots)q^{7}+\cdots\)
2070.3.c.b 2070.c 23.b $32$ $56.403$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
2070.3.c.c 2070.c 23.b $32$ $56.403$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(2070, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2070, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(46, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(69, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(138, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(230, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(345, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(414, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1035, [\chi])\)\(^{\oplus 2}\)