Properties

Label 575.2.b
Level $575$
Weight $2$
Character orbit 575.b
Rep. character $\chi_{575}(24,\cdot)$
Character field $\Q$
Dimension $34$
Newform subspaces $6$
Sturm bound $120$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 575.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(120\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(575, [\chi])\).

Total New Old
Modular forms 66 34 32
Cusp forms 54 34 20
Eisenstein series 12 0 12

Trace form

\( 34 q - 36 q^{4} + 4 q^{6} - 30 q^{9} + O(q^{10}) \) \( 34 q - 36 q^{4} + 4 q^{6} - 30 q^{9} - 8 q^{11} + 4 q^{14} + 40 q^{16} - 4 q^{19} + 8 q^{21} - 8 q^{24} - 24 q^{26} - 16 q^{29} + 20 q^{31} - 4 q^{34} + 24 q^{36} + 48 q^{41} + 52 q^{44} + 4 q^{46} - 66 q^{49} + 16 q^{51} + 36 q^{54} - 80 q^{56} - 12 q^{59} + 60 q^{61} - 60 q^{64} - 16 q^{66} - 8 q^{69} - 20 q^{71} - 28 q^{74} + 28 q^{76} - 8 q^{79} + 34 q^{81} + 68 q^{84} - 68 q^{86} - 56 q^{89} - 24 q^{91} - 60 q^{94} - 140 q^{96} + 116 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(575, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
575.2.b.a 575.b 5.b $2$ $4.591$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}+iq^{7}+3q^{9}+2q^{11}+\cdots\)
575.2.b.b 575.b 5.b $2$ $4.591$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}-iq^{7}+3iq^{8}+3q^{9}+\cdots\)
575.2.b.c 575.b 5.b $4$ $4.591$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+3\beta _{2}q^{4}+(1+\cdots)q^{6}+\cdots\)
575.2.b.d 575.b 5.b $4$ $4.591$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
575.2.b.e 575.b 5.b $8$ $4.591$ 8.0.\(\cdots\).11 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
575.2.b.f 575.b 5.b $14$ $4.591$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(-2+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(575, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)