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

Downloads

Learn more about

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

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