Properties

Label 525.2.m
Level $525$
Weight $2$
Character orbit 525.m
Rep. character $\chi_{525}(118,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
Newform subspaces $3$
Sturm bound $160$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(160\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(525, [\chi])\).

Total New Old
Modular forms 184 48 136
Cusp forms 136 48 88
Eisenstein series 48 0 48

Trace form

\( 48 q + 8 q^{7} - 24 q^{8} + O(q^{10}) \) \( 48 q + 8 q^{7} - 24 q^{8} + 32 q^{11} + 16 q^{16} + 4 q^{21} + 16 q^{22} + 40 q^{23} - 24 q^{28} - 48 q^{32} - 48 q^{36} - 32 q^{37} + 16 q^{42} + 16 q^{43} - 8 q^{46} + 32 q^{51} - 24 q^{53} - 48 q^{56} - 8 q^{57} - 32 q^{58} - 8 q^{63} + 32 q^{67} - 128 q^{71} - 24 q^{72} + 24 q^{77} + 8 q^{78} - 48 q^{81} - 8 q^{86} + 64 q^{88} - 4 q^{91} + 40 q^{92} - 24 q^{93} + 96 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
525.2.m.a 525.m 35.f $8$ $4.192$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{24}^{2}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{3}q^{4}-\zeta_{24}^{4}q^{6}+\cdots\)
525.2.m.b 525.m 35.f $16$ $4.192$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+\beta _{9}q^{3}+(\beta _{2}+\beta _{7}-\beta _{11}+\cdots)q^{4}+\cdots\)
525.2.m.c 525.m 35.f $24$ $4.192$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)