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Properties

Label 762.2.h
Level $762$
Weight $2$
Character orbit 762.h
Rep. character $\chi_{762}(401,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $2$
Sturm bound $256$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 762 = 2 \cdot 3 \cdot 127 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 762.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 381 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(256\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(762, [\chi])\).

Total New Old
Modular forms 264 88 176
Cusp forms 248 88 160
Eisenstein series 16 0 16

Trace form

\( 88 q - 88 q^{4} + 6 q^{7} + 4 q^{9} + O(q^{10}) \) \( 88 q - 88 q^{4} + 6 q^{7} + 4 q^{9} + 14 q^{13} - 2 q^{15} + 88 q^{16} + 4 q^{18} + 28 q^{19} + 16 q^{21} - 4 q^{22} + 92 q^{25} - 6 q^{28} + 2 q^{30} + 12 q^{31} + 8 q^{34} - 4 q^{36} + 22 q^{37} + 36 q^{39} + 6 q^{45} + 14 q^{49} - 14 q^{52} - 24 q^{55} + 2 q^{60} + 60 q^{61} - 88 q^{64} - 114 q^{67} - 38 q^{69} - 34 q^{70} - 4 q^{72} + 40 q^{73} - 18 q^{75} - 28 q^{76} + 30 q^{78} - 24 q^{79} - 8 q^{81} - 16 q^{82} - 16 q^{84} - 32 q^{87} + 4 q^{88} - 24 q^{90} + 6 q^{93} + 16 q^{94} + 12 q^{97} + 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(762, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
762.2.h.a 762.h 381.g $4$ $6.085$ \(\Q(\zeta_{12})\) None \(0\) \(-6\) \(0\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}^{3}q^{2}+(-2+\zeta_{12}^{2})q^{3}-q^{4}+\cdots\)
762.2.h.b 762.h 381.g $84$ $6.085$ None \(0\) \(6\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(762, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(762, [\chi]) \cong \)