Properties

Label 1575.3.f
Level $1575$
Weight $3$
Character orbit 1575.f
Rep. character $\chi_{1575}(449,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $3$
Sturm bound $720$
Trace bound $16$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1575.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(720\)
Trace bound: \(16\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1575, [\chi])\).

Total New Old
Modular forms 504 72 432
Cusp forms 456 72 384
Eisenstein series 48 0 48

Trace form

\( 72 q + 160 q^{4} + O(q^{10}) \) \( 72 q + 160 q^{4} + 80 q^{16} + 208 q^{19} + 320 q^{31} - 112 q^{34} + 96 q^{46} - 504 q^{49} + 208 q^{61} - 192 q^{64} + 1216 q^{76} + 224 q^{79} + 912 q^{94} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1575.3.f.a 1575.f 15.d $8$ $42.916$ 8.0.157351936.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}-\beta _{4}q^{4}-\beta _{1}q^{7}+(2\beta _{5}+\beta _{7})q^{8}+\cdots\)
1575.3.f.b 1575.f 15.d $32$ $42.916$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1575.3.f.c 1575.f 15.d $32$ $42.916$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(1575, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)