Properties

Label 725.2.e
Level $725$
Weight $2$
Character orbit 725.e
Rep. character $\chi_{725}(157,\cdot)$
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.e (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

\( 86 q + 4 q^{3} - 82 q^{4} + 4 q^{7} + 94 q^{9} + O(q^{10}) \) \( 86 q + 4 q^{3} - 82 q^{4} + 4 q^{7} + 94 q^{9} + 4 q^{11} + 8 q^{12} + 14 q^{13} + 16 q^{14} + 66 q^{16} - 44 q^{21} - 8 q^{22} + 4 q^{23} + 6 q^{26} + 4 q^{27} - 8 q^{28} - 28 q^{31} - 16 q^{34} - 154 q^{36} - 16 q^{37} - 8 q^{38} - 68 q^{39} - 30 q^{41} - 4 q^{42} - 12 q^{43} - 36 q^{44} - 8 q^{46} + 36 q^{47} - 4 q^{48} - 26 q^{52} - 14 q^{53} - 56 q^{56} - 12 q^{57} - 58 q^{58} - 18 q^{61} + 28 q^{62} + 60 q^{63} + 54 q^{64} + 20 q^{66} + 32 q^{67} - 12 q^{69} - 100 q^{76} - 56 q^{78} + 8 q^{79} + 190 q^{81} + 58 q^{82} + 60 q^{83} + 56 q^{84} + 12 q^{87} + 68 q^{88} - 62 q^{89} - 28 q^{92} - 8 q^{93} + 8 q^{97} - 34 q^{98} + 36 q^{99} + O(q^{100}) \)

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.e.a 725.e 145.e $4$ $5.789$ \(\Q(i, \sqrt{5})\) None 725.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{2}-3q^{4}+(-\beta _{2}+\beta _{3})q^{7}-\beta _{2}q^{8}+\cdots\)
725.2.e.b 725.e 145.e $16$ $5.789$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 725.2.e.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{7}q^{2}+\beta _{9}q^{3}-\beta _{2}q^{4}+(\beta _{4}+\beta _{6}+\cdots)q^{6}+\cdots\)
725.2.e.c 725.e 145.e $26$ $5.789$ None 145.2.e.a \(0\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$
725.2.e.d 725.e 145.e $40$ $5.789$ 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

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