Properties

Label 725.2.j
Level $725$
Weight $2$
Character orbit 725.j
Rep. character $\chi_{725}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $86$
Newform subspaces $4$
Sturm bound $150$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 725 = 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 725.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 145 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(150\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 162 94 68
Cusp forms 138 86 52
Eisenstein series 24 8 16

Trace form

\( 86 q + 6 q^{2} + 82 q^{4} + 4 q^{7} + 18 q^{8} - 94 q^{9} + O(q^{10}) \) \( 86 q + 6 q^{2} + 82 q^{4} + 4 q^{7} + 18 q^{8} - 94 q^{9} + 4 q^{11} - 14 q^{13} - 16 q^{14} + 66 q^{16} - 20 q^{17} + 18 q^{18} - 44 q^{21} + 8 q^{22} + 4 q^{23} + 6 q^{26} + 8 q^{28} - 28 q^{31} + 42 q^{32} + 16 q^{34} - 154 q^{36} + 8 q^{38} + 68 q^{39} - 30 q^{41} + 4 q^{42} + 36 q^{44} - 8 q^{46} - 26 q^{52} - 14 q^{53} - 56 q^{56} + 12 q^{57} - 28 q^{58} - 18 q^{61} - 28 q^{62} - 60 q^{63} - 54 q^{64} + 20 q^{66} - 32 q^{67} - 72 q^{68} + 12 q^{69} - 10 q^{72} + 4 q^{73} - 100 q^{76} + 12 q^{77} - 56 q^{78} - 8 q^{79} + 190 q^{81} + 58 q^{82} + 60 q^{83} - 56 q^{84} - 60 q^{87} + 68 q^{88} + 62 q^{89} + 28 q^{92} + 8 q^{93} - 36 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
725.2.j.a 725.j 145.j $4$ $5.789$ \(\Q(i, \sqrt{5})\) None 725.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{3}q^{2}+3q^{4}+(\beta _{2}-\beta _{3})q^{7}+\beta _{3}q^{8}+\cdots\)
725.2.j.b 725.j 145.j $16$ $5.789$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 725.2.e.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}+(\beta _{4}+\beta _{6}+\cdots)q^{6}+\cdots\)
725.2.j.c 725.j 145.j $26$ $5.789$ None 145.2.e.a \(6\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$
725.2.j.d 725.j 145.j $40$ $5.789$ None 725.2.e.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

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