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Properties

Label 750.2.m
Level $750$
Weight $2$
Character orbit 750.m
Rep. character $\chi_{750}(31,\cdot)$
Character field $\Q(\zeta_{25})$
Dimension $480$
Newform subspaces $4$
Sturm bound $300$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.m (of order \(25\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 125 \)
Character field: \(\Q(\zeta_{25})\)
Newform subspaces: \( 4 \)
Sturm bound: \(300\)
Trace bound: \(10\)
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 480 2600
Cusp forms 2920 480 2440
Eisenstein series 160 0 160

Trace form

\( 480 q + O(q^{10}) \) \( 480 q + 20 q^{11} + 20 q^{17} + 10 q^{18} + 20 q^{19} + 10 q^{20} + 20 q^{22} - 40 q^{23} + 10 q^{24} - 80 q^{25} + 10 q^{28} + 40 q^{29} + 20 q^{30} + 10 q^{31} + 10 q^{32} + 20 q^{33} + 30 q^{34} + 20 q^{35} + 10 q^{37} + 60 q^{41} + 10 q^{42} + 80 q^{43} + 20 q^{46} + 40 q^{47} - 80 q^{49} + 20 q^{51} + 90 q^{53} + 100 q^{55} + 40 q^{59} - 40 q^{60} + 40 q^{61} + 60 q^{62} + 20 q^{63} + 10 q^{65} + 40 q^{67} + 50 q^{70} - 160 q^{71} + 80 q^{73} + 20 q^{76} + 80 q^{77} + 40 q^{79} - 120 q^{82} + 80 q^{83} + 110 q^{85} + 20 q^{87} + 10 q^{88} + 30 q^{89} - 240 q^{91} - 60 q^{93} - 120 q^{95} + 70 q^{97} + 80 q^{98} + O(q^{100}) \)

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.m.a 750.m 125.g $100$ $5.989$ None \(0\) \(0\) \(-20\) \(5\) $\mathrm{SU}(2)[C_{25}]$
750.2.m.b 750.m 125.g $120$ $5.989$ None \(0\) \(0\) \(20\) \(-5\) $\mathrm{SU}(2)[C_{25}]$
750.2.m.c 750.m 125.g $120$ $5.989$ None \(0\) \(0\) \(20\) \(-5\) $\mathrm{SU}(2)[C_{25}]$
750.2.m.d 750.m 125.g $140$ $5.989$ None \(0\) \(0\) \(-20\) \(5\) $\mathrm{SU}(2)[C_{25}]$

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

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