Properties

Label 1575.2.d
Level $1575$
Weight $2$
Character orbit 1575.d
Rep. character $\chi_{1575}(1324,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $12$
Sturm bound $480$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1575.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
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 264 46 218
Cusp forms 216 46 170
Eisenstein series 48 0 48

Trace form

\( 46 q - 56 q^{4} + O(q^{10}) \) \( 46 q - 56 q^{4} - 4 q^{11} + 4 q^{14} + 60 q^{16} - 8 q^{19} + 64 q^{26} - 12 q^{29} + 44 q^{31} - 20 q^{34} + 40 q^{41} - 62 q^{44} + 14 q^{46} - 46 q^{49} - 6 q^{56} - 4 q^{59} + 24 q^{61} - 42 q^{64} - 24 q^{71} + 38 q^{74} - 20 q^{76} - 12 q^{79} - 62 q^{86} - 8 q^{89} - 4 q^{91} - 4 q^{94} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1575.2.d.a 1575.d 5.b $2$ $12.576$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}-iq^{7}+3iq^{8}-4q^{11}+\cdots\)
1575.2.d.b 1575.d 5.b $2$ $12.576$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}-iq^{7}+3iq^{8}-6iq^{13}+\cdots\)
1575.2.d.c 1575.d 5.b $2$ $12.576$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{4}-iq^{7}+3q^{11}+5iq^{13}+4q^{16}+\cdots\)
1575.2.d.d 1575.d 5.b $4$ $12.576$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-3q^{4}+\beta _{1}q^{7}+\beta _{2}q^{8}+(-2+\cdots)q^{11}+\cdots\)
1575.2.d.e 1575.d 5.b $4$ $12.576$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+\beta _{2}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
1575.2.d.f 1575.d 5.b $4$ $12.576$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+3\beta _{2}q^{4}-\beta _{3}q^{7}+(-4\beta _{1}+\cdots)q^{8}+\cdots\)
1575.2.d.g 1575.d 5.b $4$ $12.576$ \(\Q(i, \sqrt{13})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+\beta _{2}q^{7}+3\beta _{2}q^{8}+\cdots\)
1575.2.d.h 1575.d 5.b $4$ $12.576$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1575.2.d.i 1575.d 5.b $4$ $12.576$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{2}-q^{4}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{8}+\cdots\)
1575.2.d.j 1575.d 5.b $4$ $12.576$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
1575.2.d.k 1575.d 5.b $4$ $12.576$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{7}+(2\beta _{1}+\cdots)q^{8}+\cdots\)
1575.2.d.l 1575.d 5.b $8$ $12.576$ 8.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-2+\beta _{6})q^{4}-\beta _{4}q^{7}+(-2\beta _{2}+\cdots)q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)