Properties

Label 725.2.b
Level $725$
Weight $2$
Character orbit 725.b
Rep. character $\chi_{725}(349,\cdot)$
Character field $\Q$
Dimension $42$
Newform subspaces $7$
Sturm bound $150$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 725 = 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 725.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(150\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(725, [\chi])\).

Total New Old
Modular forms 82 42 40
Cusp forms 70 42 28
Eisenstein series 12 0 12

Trace form

\( 42 q - 34 q^{4} - 8 q^{6} - 46 q^{9} + O(q^{10}) \) \( 42 q - 34 q^{4} - 8 q^{6} - 46 q^{9} + 4 q^{11} + 4 q^{14} + 18 q^{16} + 12 q^{19} + 12 q^{21} + 56 q^{24} - 24 q^{26} - 6 q^{29} + 12 q^{31} + 56 q^{34} + 34 q^{36} - 40 q^{39} - 24 q^{41} + 36 q^{44} + 16 q^{46} - 26 q^{49} - 12 q^{51} + 44 q^{54} - 80 q^{56} + 36 q^{59} - 36 q^{61} + 26 q^{64} - 12 q^{66} - 40 q^{69} - 4 q^{71} + 36 q^{74} + 20 q^{76} + 20 q^{79} + 106 q^{81} - 60 q^{84} + 48 q^{86} - 28 q^{89} - 44 q^{91} - 64 q^{94} - 52 q^{96} + 60 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(725, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
725.2.b.a 725.b 5.b $2$ $5.789$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+q^{4}+2iq^{7}+3iq^{8}+3q^{9}+\cdots\)
725.2.b.b 725.b 5.b $4$ $5.789$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
725.2.b.c 725.b 5.b $4$ $5.789$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots\)
725.2.b.d 725.b 5.b $6$ $5.789$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+(\beta _{2}-\beta _{4})q^{3}+(-2-\beta _{3}+\cdots)q^{4}+\cdots\)
725.2.b.e 725.b 5.b $6$ $5.789$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+(\beta _{2}-\beta _{4})q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{6}+\cdots\)
725.2.b.f 725.b 5.b $10$ $5.789$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
725.2.b.g 725.b 5.b $10$ $5.789$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{2}+\beta _{7})q^{3}+(-1+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(725, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(725, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)