# Properties

 Label 2900.2.c Level $2900$ Weight $2$ Character orbit 2900.c Rep. character $\chi_{2900}(349,\cdot)$ Character field $\Q$ Dimension $42$ Newform subspaces $9$ Sturm bound $900$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$2900 = 2^{2} \cdot 5^{2} \cdot 29$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2900.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$9$$ Sturm bound: $$900$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$3$$, $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(2900, [\chi])$$.

Total New Old
Modular forms 468 42 426
Cusp forms 432 42 390
Eisenstein series 36 0 36

## Trace form

 $$42 q - 46 q^{9} + O(q^{10})$$ $$42 q - 46 q^{9} + 8 q^{11} - 8 q^{19} - 4 q^{21} + 6 q^{29} + 16 q^{31} + 8 q^{39} - 24 q^{41} - 58 q^{49} - 68 q^{51} + 12 q^{59} - 28 q^{61} + 8 q^{69} + 28 q^{71} + 16 q^{79} + 42 q^{81} - 44 q^{89} - 4 q^{91} - 24 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(2900, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2900.2.c.a $2$ $23.157$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3iq^{3}+4iq^{7}-6q^{9}-q^{11}+3iq^{13}+\cdots$$
2900.2.c.b $2$ $23.157$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}-2iq^{7}-q^{9}-6q^{11}+iq^{13}+\cdots$$
2900.2.c.c $2$ $23.157$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{3}+4iq^{7}+2q^{9}+3q^{11}+5iq^{13}+\cdots$$
2900.2.c.d $2$ $23.157$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+iq^{7}+3q^{9}-4q^{11}-3iq^{13}+2iq^{17}+\cdots$$
2900.2.c.e $2$ $23.157$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3q^{9}-2q^{11}-iq^{13}+2q^{19}-4iq^{23}+\cdots$$
2900.2.c.f $6$ $23.157$ 6.0.5089536.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{3}+(\beta _{2}+\beta _{4})q^{7}+(-4+\beta _{1}+\cdots)q^{9}+\cdots$$
2900.2.c.g $6$ $23.157$ 6.0.350464.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{5}q^{7}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots$$
2900.2.c.h $10$ $23.157$ 10.0.$$\cdots$$.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{3}-\beta _{4})q^{7}+(-1+\cdots)q^{9}+\cdots$$
2900.2.c.i $10$ $23.157$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+(\beta _{3}+\beta _{9})q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(2900, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(2900, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(50, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(100, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(145, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(290, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(580, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(725, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(1450, [\chi])$$$$^{\oplus 2}$$