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Properties

Label 725.2.r
Level $725$
Weight $2$
Character orbit 725.r
Rep. character $\chi_{725}(24,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $252$
Newform subspaces $5$
Sturm bound $150$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 725 = 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 725.r (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 145 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 5 \)
Sturm bound: \(150\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 492 276 216
Cusp forms 420 252 168
Eisenstein series 72 24 48

Trace form

\( 252 q + 48 q^{4} + 22 q^{6} + 60 q^{9} + O(q^{10}) \) \( 252 q + 48 q^{4} + 22 q^{6} + 60 q^{9} - 18 q^{11} + 10 q^{14} - 32 q^{16} + 2 q^{19} + 30 q^{21} - 98 q^{24} - 32 q^{26} - 8 q^{29} + 2 q^{31} + 56 q^{34} - 6 q^{36} + 26 q^{39} - 4 q^{41} - 134 q^{44} - 44 q^{46} - 44 q^{49} - 44 q^{51} - 30 q^{54} - 4 q^{56} + 160 q^{59} - 34 q^{61} - 12 q^{64} + 166 q^{66} - 58 q^{69} - 52 q^{71} - 134 q^{74} - 146 q^{76} - 6 q^{79} - 148 q^{81} + 382 q^{84} - 356 q^{86} + 42 q^{89} + 30 q^{91} + 92 q^{94} - 270 q^{96} - 256 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.r.a 725.r 145.n $12$ $5.789$ \(\Q(\zeta_{28})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$ \(q+(\zeta_{28}^{3}-\zeta_{28}^{5}+\zeta_{28}^{7}-\zeta_{28}^{9})q^{2}+\cdots\)
725.2.r.b 725.r 145.n $12$ $5.789$ \(\Q(\zeta_{28})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$ \(q+(-\zeta_{28}^{3}+\zeta_{28}^{9})q^{2}+(-\zeta_{28}^{7}-\zeta_{28}^{11})q^{3}+\cdots\)
725.2.r.c 725.r 145.n $48$ $5.789$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$
725.2.r.d 725.r 145.n $72$ $5.789$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$
725.2.r.e 725.r 145.n $108$ $5.789$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$

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

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