Properties

Label 1575.2.m
Level $1575$
Weight $2$
Character orbit 1575.m
Rep. character $\chi_{1575}(1268,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $6$
Sturm bound $480$
Trace bound $8$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1575.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(480\)
Trace bound: \(8\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 528 72 456
Cusp forms 432 72 360
Eisenstein series 96 0 96

Trace form

\( 72 q + O(q^{10}) \) \( 72 q + 8 q^{13} - 40 q^{16} + 16 q^{22} - 8 q^{37} - 80 q^{43} - 64 q^{46} - 72 q^{52} + 56 q^{58} + 128 q^{61} + 96 q^{67} + 40 q^{73} - 64 q^{76} - 40 q^{82} - 24 q^{97} + O(q^{100}) \)

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.m.a 1575.m 15.e $8$ $12.576$ \(\Q(\zeta_{24})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{24}^{2}q^{2}+(-1+\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
1575.2.m.b 1575.m 15.e $8$ $12.576$ \(\Q(\zeta_{24})\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{24}^{6}q^{2}+(-1+\zeta_{24}^{2}-\zeta_{24}^{6}+\cdots)q^{4}+\cdots\)
1575.2.m.c 1575.m 15.e $12$ $12.576$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{4}-2\beta _{10}+\cdots)q^{4}+\cdots\)
1575.2.m.d 1575.m 15.e $12$ $12.576$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4}+2\beta _{10})q^{4}+\cdots\)
1575.2.m.e 1575.m 15.e $16$ $12.576$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{2}-\beta _{5}-\beta _{12})q^{2}+(\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1575.2.m.f 1575.m 15.e $16$ $12.576$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{2}+\beta _{5}+\beta _{12})q^{2}+(\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)

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

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