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Properties

Label 750.2.l
Level $750$
Weight $2$
Character orbit 750.l
Rep. character $\chi_{750}(107,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $240$
Newform subspaces $3$
Sturm bound $300$
Trace bound $12$

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Defining parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 3 \)
Sturm bound: \(300\)
Trace bound: \(12\)
Distinguishing \(T_p\): \(7\), \(13\)

Dimensions

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

Total New Old
Modular forms 1360 240 1120
Cusp forms 1040 240 800
Eisenstein series 320 0 320

Trace form

\( 240 q - 4 q^{3} - 4 q^{7} + O(q^{10}) \) \( 240 q - 4 q^{3} - 4 q^{7} + 4 q^{12} + 60 q^{16} + 8 q^{18} + 40 q^{19} + 36 q^{22} - 4 q^{27} + 16 q^{28} - 4 q^{33} + 40 q^{34} + 24 q^{37} + 40 q^{39} + 4 q^{42} + 24 q^{43} + 4 q^{48} + 64 q^{57} - 20 q^{58} - 64 q^{63} - 96 q^{67} - 140 q^{69} - 8 q^{72} - 100 q^{73} - 100 q^{78} - 80 q^{79} - 120 q^{81} - 96 q^{82} - 60 q^{84} - 80 q^{87} - 4 q^{88} - 12 q^{93} + 32 q^{97} + O(q^{100}) \)

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.l.a 750.l 75.l $80$ $5.989$ None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{20}]$
750.2.l.b 750.l 75.l $80$ $5.989$ None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{20}]$
750.2.l.c 750.l 75.l $80$ $5.989$ None \(0\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{20}]$

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

\( S_{2}^{\mathrm{old}}(750, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 2}\)