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Properties

Label 440.2.z
Level $440$
Weight $2$
Character orbit 440.z
Rep. character $\chi_{440}(51,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $192$
Newform subspaces $1$
Sturm bound $144$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 440.z (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 88 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(144\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(440, [\chi])\).

Total New Old
Modular forms 304 192 112
Cusp forms 272 192 80
Eisenstein series 32 0 32

Trace form

\( 192 q - 4 q^{4} - 48 q^{9} + O(q^{10}) \) \( 192 q - 4 q^{4} - 48 q^{9} + 8 q^{11} - 10 q^{14} - 16 q^{16} - 50 q^{18} + 4 q^{20} - 56 q^{22} + 60 q^{24} + 48 q^{25} + 20 q^{26} + 50 q^{28} + 8 q^{33} - 12 q^{34} - 64 q^{36} - 50 q^{38} - 110 q^{42} + 34 q^{44} - 10 q^{46} - 14 q^{48} - 48 q^{49} - 50 q^{52} - 120 q^{56} + 62 q^{58} - 16 q^{59} - 42 q^{60} - 64 q^{64} + 54 q^{66} + 80 q^{67} - 130 q^{68} + 40 q^{70} + 50 q^{72} + 120 q^{74} + 92 q^{78} - 24 q^{80} - 64 q^{81} + 12 q^{82} + 120 q^{84} + 108 q^{86} - 8 q^{88} - 128 q^{91} + 72 q^{92} + 120 q^{94} + 170 q^{96} - 192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(440, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
440.2.z.a 440.z 88.k $192$ $3.513$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{2}^{\mathrm{old}}(440, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(440, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)