Properties

Label 750.2.e
Level $750$
Weight $2$
Character orbit 750.e
Rep. character $\chi_{750}(443,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $2$
Sturm bound $300$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 750 = 2 \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 750.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(300\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(7\)

Dimensions

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

Total New Old
Modular forms 340 64 276
Cusp forms 260 64 196
Eisenstein series 80 0 80

Trace form

\( 64 q - 4 q^{6} + O(q^{10}) \) \( 64 q - 4 q^{6} - 64 q^{16} + 8 q^{21} + 72 q^{31} - 4 q^{36} + 16 q^{46} + 112 q^{51} - 104 q^{61} - 112 q^{66} - 64 q^{76} - 12 q^{81} + 4 q^{96} + O(q^{100}) \)

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.e.a 750.e 15.e $32$ $5.989$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
750.2.e.b 750.e 15.e $32$ $5.989$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(750, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 2}\)