↑

Properties

Label 750.2.o
Level $750$
Weight $2$
Character orbit 750.o
Rep. character $\chi_{750}(19,\cdot)$
Character field $\Q(\zeta_{50})$
Dimension $520$
Newform subspaces $2$
Sturm bound $300$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.o (of order \(50\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 125 \)
Character field: \(\Q(\zeta_{50})\)
Newform subspaces: \( 2 \)
Sturm bound: \(300\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(750, [\chi])\).

Total New Old
Modular forms 3080 520 2560
Cusp forms 2920 520 2400
Eisenstein series 160 0 160

Trace form

\( 520 q + O(q^{10}) \) \( 520 q - 20 q^{11} + 20 q^{17} + 20 q^{19} + 20 q^{22} + 120 q^{23} + 10 q^{24} + 80 q^{25} + 10 q^{28} + 40 q^{29} + 20 q^{30} - 10 q^{31} + 20 q^{33} - 20 q^{34} + 20 q^{35} - 60 q^{41} - 10 q^{42} - 20 q^{46} + 40 q^{47} + 170 q^{49} - 20 q^{51} - 20 q^{55} + 40 q^{59} + 40 q^{60} - 40 q^{61} - 60 q^{62} - 20 q^{63} + 40 q^{67} + 30 q^{70} + 160 q^{71} - 20 q^{76} - 80 q^{77} + 40 q^{79} + 200 q^{82} - 40 q^{83} - 20 q^{85} + 20 q^{87} - 10 q^{88} - 20 q^{89} + 240 q^{91} + 100 q^{93} + 200 q^{95} - 50 q^{97} - 80 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(750, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
750.2.o.a 750.o 125.h $240$ $5.989$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{50}]$
750.2.o.b 750.o 125.h $280$ $5.989$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{50}]$

Decomposition of \(S_{2}^{\mathrm{old}}(750, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(750, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 2}\)