Properties

Label 1755.2.i
Level $1755$
Weight $2$
Character orbit 1755.i
Rep. character $\chi_{1755}(586,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $96$
Newform subspaces $8$
Sturm bound $504$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1755 = 3^{3} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1755.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
Sturm bound: \(504\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1755, [\chi])\).

Total New Old
Modular forms 528 96 432
Cusp forms 480 96 384
Eisenstein series 48 0 48

Trace form

\( 96 q - 4 q^{2} - 48 q^{4} - 4 q^{5} + 24 q^{8} + O(q^{10}) \) \( 96 q - 4 q^{2} - 48 q^{4} - 4 q^{5} + 24 q^{8} + 4 q^{11} + 24 q^{14} - 48 q^{16} - 24 q^{17} + 24 q^{19} - 12 q^{20} - 12 q^{22} + 12 q^{23} - 48 q^{25} + 12 q^{29} - 68 q^{32} + 24 q^{38} + 12 q^{40} + 8 q^{41} - 12 q^{43} - 112 q^{44} - 40 q^{47} - 60 q^{49} - 4 q^{50} - 32 q^{53} + 40 q^{56} + 24 q^{59} - 12 q^{61} + 176 q^{62} + 72 q^{64} - 8 q^{65} - 12 q^{67} + 48 q^{68} - 12 q^{70} + 64 q^{71} + 72 q^{73} - 48 q^{74} - 24 q^{76} - 28 q^{77} + 56 q^{80} + 24 q^{82} - 4 q^{86} - 36 q^{88} - 8 q^{89} + 68 q^{92} - 12 q^{94} - 36 q^{97} - 152 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1755, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1755.2.i.a 1755.i 9.c $2$ $14.014$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
1755.2.i.b 1755.i 9.c $2$ $14.014$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1755.2.i.c 1755.i 9.c $2$ $14.014$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1755.2.i.d 1755.i 9.c $2$ $14.014$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(4-4\zeta_{6})q^{7}-\zeta_{6}q^{13}+\cdots\)
1755.2.i.e 1755.i 9.c $16$ $14.014$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-1\) \(0\) \(8\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1-\beta _{2}-\beta _{4}+\beta _{12})q^{4}+\cdots\)
1755.2.i.f 1755.i 9.c $16$ $14.014$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(3\) \(0\) \(-8\) \(11\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{6})q^{2}+(-1+\beta _{2}-\beta _{11}+\cdots)q^{4}+\cdots\)
1755.2.i.g 1755.i 9.c $26$ $14.014$ None \(-1\) \(0\) \(13\) \(-10\) $\mathrm{SU}(2)[C_{3}]$
1755.2.i.h 1755.i 9.c $30$ $14.014$ None \(-1\) \(0\) \(-15\) \(-10\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1755, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1755, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(351, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)