Properties

Label 225.4.w
Level $225$
Weight $4$
Character orbit 225.w
Rep. character $\chi_{225}(2,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1408$
Newform subspaces $1$
Sturm bound $120$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.w (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{60})\)
Newform subspaces: \( 1 \)
Sturm bound: \(120\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 1472 1472 0
Cusp forms 1408 1408 0
Eisenstein series 64 64 0

Trace form

\( 1408 q - 24 q^{2} - 20 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} + O(q^{10}) \) \( 1408 q - 24 q^{2} - 20 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} + 118 q^{12} - 8 q^{13} - 30 q^{14} + 76 q^{15} - 2630 q^{16} + 460 q^{18} - 40 q^{19} - 408 q^{20} - 12 q^{21} + 24 q^{22} - 336 q^{23} - 584 q^{25} - 200 q^{27} + 192 q^{28} - 30 q^{29} + 1150 q^{30} - 6 q^{31} + 1740 q^{32} + 274 q^{33} - 10 q^{34} + 244 q^{36} - 176 q^{37} - 144 q^{38} - 2460 q^{39} - 136 q^{40} - 18 q^{41} - 318 q^{42} - 8 q^{43} + 1166 q^{45} - 24 q^{46} - 3492 q^{47} + 1844 q^{48} - 696 q^{50} - 32 q^{51} + 312 q^{52} + 3750 q^{54} - 324 q^{55} - 18 q^{56} + 1964 q^{57} - 544 q^{58} + 4950 q^{59} + 15802 q^{60} - 6 q^{61} + 1598 q^{63} - 40 q^{64} + 2064 q^{65} + 852 q^{66} - 620 q^{67} - 8856 q^{68} - 3100 q^{69} - 508 q^{70} - 7686 q^{72} - 32 q^{73} + 468 q^{75} - 272 q^{76} - 9864 q^{77} - 7114 q^{78} - 10 q^{79} + 628 q^{81} + 3744 q^{82} - 2844 q^{83} + 1900 q^{84} + 1648 q^{85} - 18 q^{86} - 750 q^{87} + 1328 q^{88} - 3974 q^{90} - 24 q^{91} - 13182 q^{92} - 5650 q^{93} + 8270 q^{94} - 4314 q^{95} - 1260 q^{96} - 368 q^{97} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
225.4.w.a \(1408\) \(13.275\) None \(-24\) \(-20\) \(-24\) \(-8\)