Properties

Label 1575.2.bc
Level $1575$
Weight $2$
Character orbit 1575.bc
Rep. character $\chi_{1575}(899,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $5$
Sturm bound $480$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1575.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(480\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1575, [\chi])\).

Total New Old
Modular forms 528 96 432
Cusp forms 432 96 336
Eisenstein series 96 0 96

Trace form

\( 96 q - 48 q^{4} + O(q^{10}) \) \( 96 q - 48 q^{4} - 48 q^{16} - 12 q^{19} + 24 q^{31} + 24 q^{46} - 12 q^{49} - 12 q^{61} + 96 q^{64} - 24 q^{79} + 12 q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1575.2.bc.a 1575.bc 105.p $8$ $12.576$ \(\Q(\zeta_{24})\) None 63.2.p.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}+(3\zeta_{24}-2\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
1575.2.bc.b 1575.bc 105.p $8$ $12.576$ \(\Q(\zeta_{24})\) None 1575.2.bk.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{24}^{2}q^{4}+(2\zeta_{24}+\zeta_{24}^{3})q^{7}-\zeta_{24}^{5}q^{11}+\cdots\)
1575.2.bc.c 1575.bc 105.p $24$ $12.576$ None 315.2.bj.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
1575.2.bc.d 1575.bc 105.p $24$ $12.576$ None 315.2.bj.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
1575.2.bc.e 1575.bc 105.p $32$ $12.576$ None 1575.2.bk.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)