Properties

Label 925.2.f
Level $925$
Weight $2$
Character orbit 925.f
Rep. character $\chi_{925}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $110$
Newform subspaces $6$
Sturm bound $190$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 925 = 5^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 925.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 6 \)
Sturm bound: \(190\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(925, [\chi])\).

Total New Old
Modular forms 202 118 84
Cusp forms 178 110 68
Eisenstein series 24 8 16

Trace form

\( 110 q - 4 q^{3} - 106 q^{4} - 4 q^{6} + 4 q^{7} + 32 q^{12} + 90 q^{16} + 20 q^{17} + 22 q^{18} + 12 q^{19} - 20 q^{22} - 12 q^{24} - 24 q^{26} + 20 q^{27} + 8 q^{28} + 2 q^{29} + 8 q^{31} - 8 q^{33} + 12 q^{37}+ \cdots + 128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(925, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
925.2.f.a 925.f 185.f $2$ $7.386$ \(\Q(\sqrt{-1}) \) None 185.2.f.b \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+i q^{2}+(-2 i-2)q^{3}+q^{4}+(-2 i+2)q^{6}+\cdots\)
925.2.f.b 925.f 185.f $2$ $7.386$ \(\Q(\sqrt{-1}) \) None 185.2.f.a \(0\) \(2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+i q^{2}+(i+1)q^{3}+q^{4}+(i-1)q^{6}+\cdots\)
925.2.f.c 925.f 185.f $6$ $7.386$ 6.0.350464.1 None 185.2.f.c \(0\) \(2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+(1-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{3}+\cdots\)
925.2.f.d 925.f 185.f $24$ $7.386$ None 185.2.f.d \(0\) \(-4\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{4}]$
925.2.f.e 925.f 185.f $28$ $7.386$ None 925.2.f.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
925.2.f.f 925.f 185.f $48$ $7.386$ None 925.2.f.f \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(925, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(925, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)