# Properties

 Label 25.22.b Level $25$ Weight $22$ Character orbit 25.b Rep. character $\chi_{25}(24,\cdot)$ Character field $\Q$ Dimension $30$ Newform subspaces $4$ Sturm bound $55$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$25 = 5^{2}$$ Weight: $$k$$ $$=$$ $$22$$ Character orbit: $$[\chi]$$ $$=$$ 25.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$55$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{22}(25, [\chi])$$.

Total New Old
Modular forms 56 32 24
Cusp forms 50 30 20
Eisenstein series 6 2 4

## Trace form

 $$30 q - 31784210 q^{4} - 255239990 q^{6} - 63470082940 q^{9} + O(q^{10})$$ $$30 q - 31784210 q^{4} - 255239990 q^{6} - 63470082940 q^{9} - 149672541190 q^{11} - 1353236063220 q^{14} + 21447493499330 q^{16} + 123132251000750 q^{19} - 265422927060540 q^{21} + 1205399059072050 q^{24} + 2265353373536960 q^{26} - 164569712969200 q^{29} - 4896078559515940 q^{31} - 86326069811814770 q^{34} + 140633598903855380 q^{36} + 60003763528629520 q^{39} - 139065528110673890 q^{41} + 1103009961084390830 q^{44} - 415447702239256740 q^{46} - 1686128370327626110 q^{49} + 2396382025011502810 q^{51} - 162900238716610750 q^{54} - 7967681652412253700 q^{56} - 13315331503103310800 q^{59} - 21290087250584988140 q^{61} + 63374731145627475390 q^{64} - 155370579097575860230 q^{66} + 132596534411275324020 q^{69} - 140630609799154103840 q^{71} - 129335238840968771020 q^{74} - 694971214354978029150 q^{76} + 91683993735331179700 q^{79} - 973121420827319371370 q^{81} + 1114612598573483635980 q^{84} - 2278666698907408513240 q^{86} - 186508365879341918850 q^{89} - 2053013957212899420440 q^{91} + 3943532697562118094280 q^{94} - 9174408855691666335490 q^{96} + 1599274032036566714620 q^{99} + O(q^{100})$$

## Decomposition of $$S_{22}^{\mathrm{new}}(25, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
25.22.b.a $2$ $69.869$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+12^{2}iq^{2}-64422iq^{3}+2014208q^{4}+\cdots$$
25.22.b.b $6$ $69.869$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-2\beta _{1}-\beta _{4})q^{2}+(-68\beta _{1}+7\beta _{4}+\cdots)q^{3}+\cdots$$
25.22.b.c $8$ $69.869$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{4}-\beta _{5})q^{2}+(-14\beta _{4}+11\beta _{5}+\cdots)q^{3}+\cdots$$
25.22.b.d $14$ $69.869$ $$\mathbb{Q}[x]/(x^{14} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{7}q^{2}+(-\beta _{7}+\beta _{9})q^{3}+(-1107130+\cdots)q^{4}+\cdots$$

## Decomposition of $$S_{22}^{\mathrm{old}}(25, [\chi])$$ into lower level spaces

$$S_{22}^{\mathrm{old}}(25, [\chi]) \simeq$$ $$S_{22}^{\mathrm{new}}(5, [\chi])$$$$^{\oplus 2}$$