# Properties

 Label 25.10.a Level $25$ Weight $10$ Character orbit 25.a Rep. character $\chi_{25}(1,\cdot)$ Character field $\Q$ Dimension $13$ Newform subspaces $5$ Sturm bound $25$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$25 = 5^{2}$$ Weight: $$k$$ $$=$$ $$10$$ Character orbit: $$[\chi]$$ $$=$$ 25.a (trivial) Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$25$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{10}(\Gamma_0(25))$$.

Total New Old
Modular forms 25 16 9
Cusp forms 19 13 6
Eisenstein series 6 3 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$$5$$Dim.
$$+$$$$6$$
$$-$$$$7$$

## Trace form

 $$13q + 18q^{2} - 146q^{3} + 2646q^{4} + 5226q^{6} - 5942q^{7} + 12600q^{8} + 100659q^{9} + O(q^{10})$$ $$13q + 18q^{2} - 146q^{3} + 2646q^{4} + 5226q^{6} - 5942q^{7} + 12600q^{8} + 100659q^{9} - 21654q^{11} - 227152q^{12} + 914q^{13} + 496092q^{14} + 88658q^{16} - 907662q^{17} + 1008394q^{18} + 969310q^{19} - 625704q^{21} - 4083944q^{22} + 1581774q^{23} + 4292430q^{24} + 1682796q^{26} - 313100q^{27} - 3305504q^{28} + 8412090q^{29} - 3791464q^{31} + 4067808q^{32} - 717232q^{33} - 20191978q^{34} + 11989128q^{36} + 36053298q^{37} - 3821400q^{38} - 68889252q^{39} - 20836944q^{41} + 61126176q^{42} - 46492906q^{43} - 69751518q^{44} + 15848116q^{46} - 22853022q^{47} + 38239424q^{48} + 24808241q^{49} - 21884514q^{51} - 139262232q^{52} - 703446q^{53} + 376027710q^{54} - 34468740q^{56} - 87911000q^{57} + 231081500q^{58} + 331989780q^{59} + 382273346q^{61} - 331039104q^{62} - 198326886q^{63} - 13129534q^{64} - 664225158q^{66} + 45604738q^{67} + 265631256q^{68} - 496002792q^{69} + 350390916q^{71} + 139728600q^{72} - 533029126q^{73} - 1040528568q^{74} - 635216430q^{76} + 996146736q^{77} + 794572208q^{78} + 209911540q^{79} + 1967863233q^{81} + 268068116q^{82} - 1664055066q^{83} + 336212532q^{84} - 2469223944q^{86} + 523405300q^{87} + 368023200q^{88} + 185130720q^{89} + 3029536716q^{91} + 700560288q^{92} + 31047288q^{93} - 934995088q^{94} - 3330236994q^{96} - 618891222q^{97} + 621046626q^{98} - 2710421172q^{99} + O(q^{100})$$

## Decomposition of $$S_{10}^{\mathrm{new}}(\Gamma_0(25))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 5
25.10.a.a $$1$$ $$12.876$$ $$\Q$$ None $$8$$ $$114$$ $$0$$ $$-4242$$ $$+$$ $$q+8q^{2}+114q^{3}-448q^{4}+912q^{6}+\cdots$$
25.10.a.b $$2$$ $$12.876$$ $$\Q(\sqrt{1009})$$ None $$10$$ $$-260$$ $$0$$ $$-1700$$ $$+$$ $$q+(5-\beta )q^{2}+(-130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots$$
25.10.a.c $$3$$ $$12.876$$ $$\mathbb{Q}[x]/(x^{3} - \cdots)$$ None $$-33$$ $$-89$$ $$0$$ $$-5258$$ $$+$$ $$q+(-11-\beta _{1})q^{2}+(-30-2\beta _{1}+\beta _{2})q^{3}+\cdots$$
25.10.a.d $$3$$ $$12.876$$ $$\mathbb{Q}[x]/(x^{3} - \cdots)$$ None $$33$$ $$89$$ $$0$$ $$5258$$ $$-$$ $$q+(11+\beta _{1})q^{2}+(30+2\beta _{1}-\beta _{2})q^{3}+\cdots$$
25.10.a.e $$4$$ $$12.876$$ 4.4.49740556.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$-$$ $$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(342-\beta _{3})q^{4}+\cdots$$

## Decomposition of $$S_{10}^{\mathrm{old}}(\Gamma_0(25))$$ into lower level spaces

$$S_{10}^{\mathrm{old}}(\Gamma_0(25)) \cong$$ $$S_{10}^{\mathrm{new}}(\Gamma_0(5))$$$$^{\oplus 2}$$