Properties

Label 525.3.f
Level $525$
Weight $3$
Character orbit 525.f
Rep. character $\chi_{525}(449,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $3$
Sturm bound $240$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 525.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(240\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(525, [\chi])\).

Total New Old
Modular forms 172 72 100
Cusp forms 148 72 76
Eisenstein series 24 0 24

Trace form

\( 72 q + 136 q^{4} + 24 q^{9} + O(q^{10}) \) \( 72 q + 136 q^{4} + 24 q^{9} + 392 q^{16} - 104 q^{19} - 28 q^{21} + 172 q^{24} - 40 q^{31} + 128 q^{34} - 132 q^{36} - 44 q^{39} + 288 q^{46} - 504 q^{49} - 160 q^{51} - 380 q^{54} - 464 q^{61} + 1488 q^{64} - 748 q^{66} - 468 q^{69} + 16 q^{76} - 136 q^{79} + 496 q^{81} - 224 q^{84} + 168 q^{91} - 936 q^{94} + 852 q^{96} + 656 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
525.3.f.a 525.f 15.d $8$ $14.305$ 8.0.4337012736.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-\beta _{2}+\beta _{3}+\beta _{4})q^{3}+(3+\cdots)q^{4}+\cdots\)
525.3.f.b 525.f 15.d $32$ $14.305$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
525.3.f.c 525.f 15.d $32$ $14.305$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

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