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Properties

Label 225.3.r
Level $225$
Weight $3$
Character orbit 225.r
Rep. character $\chi_{225}(28,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $192$
Newform subspaces $3$
Sturm bound $90$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 225.r (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 3 \)
Sturm bound: \(90\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(225, [\chi])\).

Total New Old
Modular forms 512 208 304
Cusp forms 448 192 256
Eisenstein series 64 16 48

Trace form

\( 192 q + 6 q^{2} - 10 q^{4} + 6 q^{5} + 6 q^{7} + 22 q^{8} + O(q^{10}) \) \( 192 q + 6 q^{2} - 10 q^{4} + 6 q^{5} + 6 q^{7} + 22 q^{8} + 6 q^{10} + 6 q^{11} - 18 q^{13} + 10 q^{14} + 162 q^{16} + 40 q^{17} - 110 q^{19} + 114 q^{20} - 10 q^{22} + 86 q^{23} + 24 q^{25} + 36 q^{26} + 166 q^{28} - 90 q^{29} - 6 q^{31} - 346 q^{32} - 60 q^{34} - 140 q^{35} - 54 q^{37} + 244 q^{38} + 272 q^{40} - 74 q^{41} + 198 q^{43} + 360 q^{44} - 6 q^{46} + 218 q^{47} + 84 q^{50} - 280 q^{52} - 114 q^{53} - 26 q^{55} + 70 q^{56} - 328 q^{58} - 540 q^{59} + 114 q^{61} - 1272 q^{62} - 1260 q^{64} - 632 q^{65} - 370 q^{67} - 814 q^{68} - 570 q^{70} + 66 q^{71} - 346 q^{73} - 80 q^{76} + 338 q^{77} + 190 q^{79} + 1014 q^{80} - 378 q^{82} + 1264 q^{83} + 368 q^{85} + 6 q^{86} + 78 q^{88} + 1510 q^{89} - 6 q^{91} + 1534 q^{92} + 390 q^{94} + 474 q^{95} - 250 q^{97} - 78 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
225.3.r.a 225.r 25.f $32$ $6.131$ None \(10\) \(0\) \(10\) \(-10\) $\mathrm{SU}(2)[C_{20}]$
225.3.r.b 225.r 25.f $80$ $6.131$ None \(-4\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{20}]$
225.3.r.c 225.r 25.f $80$ $6.131$ None \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{3}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(225, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)