Properties

Label 224.3.v
Level $224$
Weight $3$
Character orbit 224.v
Rep. character $\chi_{224}(13,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $248$
Newform subspaces $2$
Sturm bound $96$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 224 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(224, [\chi])\).

Total New Old
Modular forms 264 264 0
Cusp forms 248 248 0
Eisenstein series 16 16 0

Trace form

\( 248 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} + O(q^{10}) \) \( 248 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{11} + 12 q^{14} + 12 q^{16} - 68 q^{18} - 4 q^{21} - 44 q^{22} + 56 q^{23} - 8 q^{25} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 8 q^{32} + 92 q^{35} + 192 q^{36} - 8 q^{37} - 8 q^{39} - 424 q^{42} - 104 q^{43} + 308 q^{44} - 8 q^{46} - 320 q^{50} - 80 q^{51} - 168 q^{53} + 356 q^{56} - 8 q^{57} - 712 q^{58} + 264 q^{60} - 8 q^{63} - 272 q^{64} - 16 q^{65} - 168 q^{67} + 320 q^{70} + 504 q^{71} - 8 q^{72} + 124 q^{74} - 4 q^{77} + 560 q^{78} - 1000 q^{84} - 208 q^{85} - 8 q^{86} - 800 q^{88} + 188 q^{91} + 852 q^{92} + 64 q^{93} - 16 q^{95} - 376 q^{98} + 64 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(224, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
224.3.v.a 224.v 224.v $8$ $6.104$ 8.0.157351936.1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{8}]$ \(q+(2\beta _{6}-\beta _{7})q^{2}+(-\beta _{3}+3\beta _{5})q^{4}+\cdots\)
224.3.v.b 224.v 224.v $240$ $6.104$ None \(-8\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{8}]$