# Properties

 Label 1925.2.b Level $1925$ Weight $2$ Character orbit 1925.b Rep. character $\chi_{1925}(1849,\cdot)$ Character field $\Q$ Dimension $88$ Newform subspaces $18$ Sturm bound $480$ Trace bound $11$

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## Defining parameters

 Level: $$N$$ $$=$$ $$1925 = 5^{2} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1925.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$18$$ Sturm bound: $$480$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$2$$, $$3$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1925, [\chi])$$.

Total New Old
Modular forms 252 88 164
Cusp forms 228 88 140
Eisenstein series 24 0 24

## Trace form

 $$88 q - 100 q^{4} + 16 q^{6} - 76 q^{9} + O(q^{10})$$ $$88 q - 100 q^{4} + 16 q^{6} - 76 q^{9} - 8 q^{11} + 8 q^{14} + 124 q^{16} - 32 q^{19} + 8 q^{24} - 24 q^{26} + 40 q^{29} + 20 q^{31} - 40 q^{34} + 68 q^{36} - 16 q^{39} - 16 q^{41} + 20 q^{44} + 80 q^{46} - 88 q^{49} + 24 q^{51} + 40 q^{54} - 24 q^{56} - 44 q^{59} - 196 q^{64} - 36 q^{69} - 44 q^{71} + 208 q^{76} - 24 q^{79} + 8 q^{81} - 40 q^{86} + 108 q^{89} - 16 q^{91} - 16 q^{94} - 80 q^{96} + 44 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1925, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1925.2.b.a $2$ $15.371$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{2}-2q^{4}-iq^{7}+3q^{9}+q^{11}+\cdots$$
1925.2.b.b $2$ $15.371$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}+q^{4}+iq^{7}+3iq^{8}+3q^{9}+\cdots$$
1925.2.b.c $2$ $15.371$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-2iq^{3}+q^{4}+2q^{6}-iq^{7}+\cdots$$
1925.2.b.d $2$ $15.371$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{2}-2iq^{3}+q^{4}+2q^{6}-iq^{7}+\cdots$$
1925.2.b.e $2$ $15.371$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{3}+2q^{4}-iq^{7}-6q^{9}-q^{11}+\cdots$$
1925.2.b.f $2$ $15.371$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2iq^{3}+2q^{4}+iq^{7}-q^{9}-q^{11}+\cdots$$
1925.2.b.g $2$ $15.371$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-iq^{3}+2q^{4}+iq^{7}+2q^{9}-q^{11}+\cdots$$
1925.2.b.h $4$ $15.371$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-3q^{4}+(-5+\cdots)q^{6}+\cdots$$
1925.2.b.i $4$ $15.371$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$$
1925.2.b.j $4$ $15.371$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\zeta_{8}+\zeta_{8}^{2})q^{2}-\zeta_{8}^{2}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots$$
1925.2.b.k $4$ $15.371$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{2}q^{2}+(\zeta_{12}-\zeta_{12}^{2})q^{3}-q^{4}+\cdots$$
1925.2.b.l $4$ $15.371$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$$
1925.2.b.m $6$ $15.371$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots$$
1925.2.b.n $6$ $15.371$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}+\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots$$
1925.2.b.o $6$ $15.371$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}-\beta _{5}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots$$
1925.2.b.p $8$ $15.371$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{4}-\beta _{6})q^{2}-\beta _{7}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots$$
1925.2.b.q $14$ $15.371$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-2-\beta _{7}+\beta _{8}+\cdots)q^{4}+\cdots$$
1925.2.b.r $14$ $15.371$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-2+\beta _{2})q^{4}-\beta _{10}q^{6}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1925, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1925, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(55, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(275, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(385, [\chi])$$$$^{\oplus 2}$$