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Properties

Label 225.4.m
Level $225$
Weight $4$
Character orbit 225.m
Rep. character $\chi_{225}(19,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $144$
Newform subspaces $3$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.m (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 376 152 224
Cusp forms 344 144 200
Eisenstein series 32 8 24

Trace form

\( 144 q + 5 q^{2} + 133 q^{4} - 9 q^{5} - 100 q^{8} + O(q^{10}) \) \( 144 q + 5 q^{2} + 133 q^{4} - 9 q^{5} - 100 q^{8} + 31 q^{10} + q^{11} - 5 q^{13} + 101 q^{14} - 607 q^{16} - 155 q^{17} - 43 q^{19} + 9 q^{20} - 690 q^{22} + 85 q^{23} + 109 q^{25} + 474 q^{26} - 45 q^{28} + 479 q^{29} - 195 q^{31} - 95 q^{34} - 1350 q^{35} - 520 q^{37} - 2745 q^{38} + 542 q^{40} - 767 q^{41} + 1178 q^{44} - 903 q^{46} + 1815 q^{47} - 5764 q^{49} + 1479 q^{50} + 2040 q^{52} + 2590 q^{53} + 549 q^{55} - 460 q^{56} + 2610 q^{58} + 513 q^{59} + 765 q^{61} - 1950 q^{62} + 1908 q^{64} - 1412 q^{65} + 3475 q^{67} - 1650 q^{70} - 1041 q^{71} + 835 q^{73} - 6504 q^{74} - 3736 q^{76} - 4990 q^{77} - 689 q^{79} + 4114 q^{80} - 4755 q^{83} - 962 q^{85} - 99 q^{86} + 870 q^{88} + 3652 q^{89} + 2282 q^{91} + 7140 q^{92} + 1693 q^{94} + 6339 q^{95} - 7835 q^{97} + 1840 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
225.4.m.a 225.m 25.e $24$ $13.275$ None \(5\) \(0\) \(-15\) \(0\) $\mathrm{SU}(2)[C_{10}]$
225.4.m.b 225.m 25.e $56$ $13.275$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
225.4.m.c 225.m 25.e $64$ $13.275$ None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{10}]$

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

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