Properties

Label 225.4.h
Level $225$
Weight $4$
Character orbit 225.h
Rep. character $\chi_{225}(46,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $148$
Newform subspaces $4$
Sturm bound $120$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(225, [\chi])\).

Total New Old
Modular forms 376 156 220
Cusp forms 344 148 196
Eisenstein series 32 8 24

Trace form

\( 148 q + 5 q^{2} - 151 q^{4} + 20 q^{5} + 8 q^{7} + 74 q^{8} + O(q^{10}) \) \( 148 q + 5 q^{2} - 151 q^{4} + 20 q^{5} + 8 q^{7} + 74 q^{8} + 35 q^{10} + 5 q^{11} + 117 q^{13} + 149 q^{14} - 471 q^{16} - 89 q^{17} - 43 q^{19} - 335 q^{20} - 392 q^{22} - q^{23} + 720 q^{25} - 678 q^{26} + 419 q^{28} + 349 q^{29} + 189 q^{31} - 738 q^{32} - 93 q^{34} - 50 q^{35} - 327 q^{37} - 527 q^{38} - 2050 q^{40} + 1003 q^{41} + 404 q^{43} + 1146 q^{44} + 897 q^{46} - 367 q^{47} + 6192 q^{49} + 2245 q^{50} + 1684 q^{52} - 801 q^{53} + 1345 q^{55} + 210 q^{56} - 3926 q^{58} + 513 q^{59} + 59 q^{61} + 2274 q^{62} - 1916 q^{64} + 2145 q^{65} - 1931 q^{67} - 3470 q^{68} - 4960 q^{70} + 2287 q^{71} - 3939 q^{73} - 5316 q^{74} + 3976 q^{76} - 1976 q^{77} - 689 q^{79} - 8940 q^{80} + 1806 q^{82} - 645 q^{83} - 1495 q^{85} + 105 q^{86} + 7496 q^{88} + 1307 q^{89} - 2288 q^{91} + 6882 q^{92} + 3585 q^{94} + 2795 q^{95} - 241 q^{97} + 13462 q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(225, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
225.4.h.a 225.h 25.d $28$ $13.275$ None 75.4.g.b \(0\) \(0\) \(15\) \(-54\) $\mathrm{SU}(2)[C_{5}]$
225.4.h.b 225.h 25.d $28$ $13.275$ None 25.4.d.a \(1\) \(0\) \(20\) \(-16\) $\mathrm{SU}(2)[C_{5}]$
225.4.h.c 225.h 25.d $28$ $13.275$ None 75.4.g.a \(4\) \(0\) \(-15\) \(58\) $\mathrm{SU}(2)[C_{5}]$
225.4.h.d 225.h 25.d $64$ $13.275$ None 225.4.h.d \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{4}^{\mathrm{old}}(225, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(225, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)