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Properties

Label 753.2.h
Level $753$
Weight $2$
Character orbit 753.h
Rep. character $\chi_{753}(32,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $328$
Newform subspaces $1$
Sturm bound $168$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 753 = 3 \cdot 251 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 753.h (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 753 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(168\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(753, [\chi])\).

Total New Old
Modular forms 344 344 0
Cusp forms 328 328 0
Eisenstein series 16 16 0

Trace form

\( 328 q - 8 q^{3} + 304 q^{4} - 15 q^{6} - 12 q^{7} + O(q^{10}) \) \( 328 q - 8 q^{3} + 304 q^{4} - 15 q^{6} - 12 q^{7} - 21 q^{12} - 6 q^{13} - 7 q^{15} + 256 q^{16} - 15 q^{18} - 10 q^{19} - 3 q^{21} - 28 q^{22} - 15 q^{24} - 288 q^{25} + 4 q^{27} - 64 q^{28} + 25 q^{30} - 14 q^{31} - 20 q^{33} + 10 q^{34} - 65 q^{36} - 10 q^{37} - 14 q^{39} - 65 q^{42} + 50 q^{43} + 18 q^{45} - 90 q^{46} - 60 q^{48} - 82 q^{49} - 46 q^{51} - 8 q^{52} - 5 q^{54} + 20 q^{55} - 20 q^{57} + 6 q^{58} + 64 q^{60} + 10 q^{61} + 46 q^{63} + 196 q^{64} + 95 q^{66} + 8 q^{67} - 20 q^{69} + 240 q^{70} - 75 q^{72} + 32 q^{73} + 131 q^{75} - 70 q^{76} - 55 q^{78} - 72 q^{79} + 16 q^{81} - 90 q^{82} - 92 q^{84} + 40 q^{85} + 50 q^{87} - 68 q^{88} + 85 q^{90} + 108 q^{91} - 8 q^{93} - 52 q^{94} - 90 q^{96} - 40 q^{97} + 65 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(753, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
753.2.h.a 753.h 753.h $328$ $6.013$ None \(0\) \(-8\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{10}]$