Properties

Label 2700.2.d
Level $2700$
Weight $2$
Character orbit 2700.d
Rep. character $\chi_{2700}(649,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $12$
Sturm bound $1080$
Trace bound $31$

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Defining parameters

Level: \( N \) \(=\) \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2700.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(1080\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2700, [\chi])\).

Total New Old
Modular forms 594 24 570
Cusp forms 486 24 462
Eisenstein series 108 0 108

Trace form

\( 24 q + O(q^{10}) \) \( 24 q + 6 q^{19} - 6 q^{31} - 66 q^{49} - 18 q^{61} + 36 q^{79} + 78 q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2700.2.d.a 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}-6q^{11}-iq^{13}+q^{19}-6iq^{23}+\cdots\)
2700.2.d.b 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{7}-6q^{11}-4iq^{13}-3iq^{17}+\cdots\)
2700.2.d.c 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-3q^{11}+iq^{13}-6iq^{17}+\cdots\)
2700.2.d.d 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4iq^{7}-7iq^{13}-8q^{19}-7q^{31}+\cdots\)
2700.2.d.e 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-2iq^{13}+3iq^{17}-5q^{19}+\cdots\)
2700.2.d.f 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}-2iq^{13}-3iq^{17}-5q^{19}+\cdots\)
2700.2.d.g 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+5iq^{7}+7iq^{13}+q^{19}-4q^{31}+\cdots\)
2700.2.d.h 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+5iq^{7}-2iq^{13}+q^{19}+11q^{31}+\cdots\)
2700.2.d.i 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{7}+2iq^{13}+7q^{19}-7q^{31}+\cdots\)
2700.2.d.j 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}+3q^{11}+iq^{13}+6iq^{17}+\cdots\)
2700.2.d.k 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+6q^{11}-iq^{13}+q^{19}+6iq^{23}+\cdots\)
2700.2.d.l 2700.d 5.b $2$ $21.560$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{7}+6q^{11}-4iq^{13}+3iq^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(180, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 2}\)