↑

Properties

Label 751.2.d
Level $751$
Weight $2$
Character orbit 751.d
Rep. character $\chi_{751}(80,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $244$
Newform subspaces $3$
Sturm bound $125$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 751.d (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 751 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 3 \)
Sturm bound: \(125\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(751, [\chi])\).

Total New Old
Modular forms 252 252 0
Cusp forms 244 244 0
Eisenstein series 8 8 0

Trace form

\( 244 q - 6 q^{2} - 4 q^{3} - 60 q^{4} - q^{5} - 3 q^{6} + 9 q^{7} + 8 q^{8} - 59 q^{9} + O(q^{10}) \) \( 244 q - 6 q^{2} - 4 q^{3} - 60 q^{4} - q^{5} - 3 q^{6} + 9 q^{7} + 8 q^{8} - 59 q^{9} - 7 q^{10} - 16 q^{11} + 9 q^{12} - 18 q^{13} + 21 q^{14} + 3 q^{15} - 94 q^{16} + 3 q^{17} + 33 q^{18} + 17 q^{19} + 21 q^{20} + 23 q^{21} + 22 q^{22} + 22 q^{23} + 23 q^{24} - 64 q^{25} - 4 q^{26} + 11 q^{27} - 48 q^{28} + 21 q^{29} - 5 q^{30} + 9 q^{31} - 10 q^{32} - 22 q^{33} + 32 q^{34} + 39 q^{35} - 41 q^{36} - 28 q^{37} - 4 q^{38} + 7 q^{39} + 2 q^{40} - 56 q^{41} - 83 q^{42} + 45 q^{43} - 33 q^{44} + 2 q^{45} - 6 q^{46} - 7 q^{47} + 54 q^{48} - 12 q^{49} + 53 q^{50} - 62 q^{51} - 4 q^{52} - 8 q^{53} + 55 q^{54} + 38 q^{55} + 23 q^{56} - 33 q^{57} + 48 q^{58} + 2 q^{59} - 92 q^{60} + 44 q^{61} + 42 q^{62} + 24 q^{63} - 102 q^{64} - 52 q^{65} + 45 q^{66} - 9 q^{67} + 69 q^{68} + 50 q^{69} - 34 q^{70} - 52 q^{71} + 202 q^{72} - 74 q^{73} - 18 q^{74} + 45 q^{75} + 74 q^{76} - 83 q^{77} - 60 q^{78} + 47 q^{79} - 66 q^{80} - 57 q^{81} + 46 q^{82} - 84 q^{83} + 97 q^{84} - 18 q^{85} - 12 q^{86} - 3 q^{87} + 55 q^{88} - 47 q^{89} + 221 q^{90} + 46 q^{91} - 110 q^{92} - 99 q^{93} + 59 q^{94} + 4 q^{95} + 214 q^{96} + 39 q^{97} + 46 q^{98} - 79 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(751, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
751.2.d.a 751.d 751.d $4$ $5.997$ \(\Q(\zeta_{10})\) None \(-3\) \(-4\) \(4\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}^{3})q^{2}+(-2+\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
751.2.d.b 751.d 751.d $4$ $5.997$ \(\Q(\zeta_{10})\) None \(-3\) \(-2\) \(-1\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}^{3})q^{2}+(-2+2\zeta_{10}-2\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)
751.2.d.c 751.d 751.d $236$ $5.997$ None \(0\) \(2\) \(-4\) \(9\) $\mathrm{SU}(2)[C_{5}]$