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Properties

Label 2700.3.p
Level $2700$
Weight $3$
Character orbit 2700.p
Rep. character $\chi_{2700}(1601,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $76$
Newform subspaces $6$
Sturm bound $1620$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2700.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(1620\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2700, [\chi])\).

Total New Old
Modular forms 2268 76 2192
Cusp forms 2052 76 1976
Eisenstein series 216 0 216

Trace form

\( 76 q - q^{7} + O(q^{10}) \) \( 76 q - q^{7} + 5 q^{13} + 2 q^{19} + 45 q^{23} - 9 q^{29} + 23 q^{31} + 20 q^{37} - 54 q^{41} - 46 q^{43} + 135 q^{47} - 255 q^{49} - 324 q^{59} - 55 q^{61} + 38 q^{67} + 86 q^{73} - 153 q^{77} - 49 q^{79} - 279 q^{83} - 134 q^{91} + 98 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2700.3.p.a 2700.p 9.d $4$ $73.570$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-4\beta _{1}-\beta _{2})q^{7}+(-2+\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
2700.3.p.b 2700.p 9.d $4$ $73.570$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(0\) \(0\) \(0\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2\beta _{1}+\beta _{2}-\beta _{3})q^{7}+(5-7\beta _{2}-2\beta _{3})q^{11}+\cdots\)
2700.3.p.c 2700.p 9.d $12$ $73.570$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2+\beta _{1}-\beta _{3}+\beta _{4})q^{7}+(-2+3\beta _{1}+\cdots)q^{11}+\cdots\)
2700.3.p.d 2700.p 9.d $16$ $73.570$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{7}q^{7}+\beta _{10}q^{11}+(\beta _{1}-\beta _{2})q^{13}+\cdots\)
2700.3.p.e 2700.p 9.d $16$ $73.570$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{7}q^{7}+\beta _{10}q^{11}+(-\beta _{1}+\beta _{2})q^{13}+\cdots\)
2700.3.p.f 2700.p 9.d $24$ $73.570$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 2}\)