Properties

Label 1875.2.b
Level $1875$
Weight $2$
Character orbit 1875.b
Rep. character $\chi_{1875}(1249,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $8$
Sturm bound $500$
Trace bound $4$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1875 = 3 \cdot 5^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1875.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(500\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1875, [\chi])\).

Total New Old
Modular forms 280 80 200
Cusp forms 220 80 140
Eisenstein series 60 0 60

Trace form

\( 80 q - 80 q^{4} - 80 q^{9} + O(q^{10}) \) \( 80 q - 80 q^{4} - 80 q^{9} + 80 q^{16} - 10 q^{19} + 10 q^{21} - 20 q^{26} + 20 q^{29} + 10 q^{31} + 20 q^{34} + 80 q^{36} - 10 q^{39} - 20 q^{41} - 60 q^{44} + 60 q^{46} - 90 q^{49} + 60 q^{56} - 10 q^{61} - 140 q^{64} - 40 q^{74} + 40 q^{76} - 40 q^{79} + 80 q^{81} - 40 q^{84} + 60 q^{86} + 20 q^{89} + 50 q^{91} + 40 q^{94} - 40 q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1875, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1875.2.b.a 1875.b 5.b $4$ $14.972$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}-\beta _{2}q^{6}+\cdots\)
1875.2.b.b 1875.b 5.b $4$ $14.972$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-\beta _{3}q^{3}+q^{4}+q^{6}+(-4\beta _{1}+\cdots)q^{7}+\cdots\)
1875.2.b.c 1875.b 5.b $8$ $14.972$ 8.0.\(\cdots\).12 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(-2+\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
1875.2.b.d 1875.b 5.b $8$ $14.972$ 8.0.324000000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{3}-\beta _{7})q^{2}+\beta _{5}q^{3}-\beta _{4}q^{4}+\cdots\)
1875.2.b.e 1875.b 5.b $12$ $14.972$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-2+\beta _{2})q^{4}+\beta _{11}q^{6}+\cdots\)
1875.2.b.f 1875.b 5.b $12$ $14.972$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(-1+\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
1875.2.b.g 1875.b 5.b $16$ $14.972$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{2}+\beta _{11}q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
1875.2.b.h 1875.b 5.b $16$ $14.972$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{9})q^{2}-\beta _{9}q^{3}+(-1-\beta _{14}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1875, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1875, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(625, [\chi])\)\(^{\oplus 2}\)