Properties

 Label 1205.2.a Level $1205$ Weight $2$ Character orbit 1205.a Rep. character $\chi_{1205}(1,\cdot)$ Character field $\Q$ Dimension $81$ Newform subspaces $5$ Sturm bound $242$ Trace bound $2$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$1205 = 5 \cdot 241$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1205.a (trivial) Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$242$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$2$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_0(1205))$$.

Total New Old
Modular forms 122 81 41
Cusp forms 119 81 38
Eisenstein series 3 0 3

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

$$5$$$$241$$FrickeDim.
$$+$$$$+$$$$+$$$$15$$
$$+$$$$-$$$$-$$$$25$$
$$-$$$$+$$$$-$$$$25$$
$$-$$$$-$$$$+$$$$16$$
Plus space$$+$$$$31$$
Minus space$$-$$$$50$$

Trace form

 $$81q - q^{2} + 4q^{3} + 83q^{4} + q^{5} + 4q^{7} - 9q^{8} + 89q^{9} + O(q^{10})$$ $$81q - q^{2} + 4q^{3} + 83q^{4} + q^{5} + 4q^{7} - 9q^{8} + 89q^{9} + 3q^{10} - 4q^{11} + 16q^{12} + 6q^{13} + 4q^{14} + 75q^{16} - 2q^{17} - 9q^{18} + 20q^{19} - q^{20} + 12q^{21} - 8q^{23} + 20q^{24} + 81q^{25} - 38q^{26} + 16q^{27} + 8q^{28} - 2q^{29} - 4q^{30} + 16q^{31} - 29q^{32} + 24q^{33} + 10q^{34} - 4q^{35} + 107q^{36} + 2q^{37} - 16q^{38} - 20q^{39} + 15q^{40} + 14q^{41} - 12q^{42} + 8q^{43} - 60q^{44} + 5q^{45} + 4q^{46} - 4q^{47} + 44q^{48} + 101q^{49} - q^{50} + 4q^{51} + 14q^{52} - 34q^{53} - 28q^{54} - 4q^{55} + 12q^{56} + 36q^{57} - 26q^{58} - 28q^{59} - 16q^{60} + 10q^{61} - 12q^{62} - 8q^{63} + 71q^{64} + 2q^{65} - 56q^{66} - 10q^{68} - 28q^{69} - 12q^{70} - 52q^{71} - 125q^{72} + 22q^{73} - 62q^{74} + 4q^{75} + 76q^{76} - 60q^{77} - 48q^{78} - 40q^{79} - q^{80} + 129q^{81} - 82q^{82} + 52q^{83} - 40q^{84} - 2q^{85} + 4q^{86} - 4q^{87} - 64q^{88} + 22q^{89} + 23q^{90} + 40q^{91} - 40q^{92} - 8q^{93} - 48q^{94} - 20q^{95} - 44q^{96} - 2q^{97} - 93q^{98} + 12q^{99} + O(q^{100})$$

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_0(1205))$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces A-L signs $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$ 5 241
1205.2.a.a $$5$$ $$9.622$$ 5.5.38569.1 None $$-1$$ $$-5$$ $$5$$ $$-10$$ $$-$$ $$-$$ $$q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots$$
1205.2.a.b $$11$$ $$9.622$$ $$\mathbb{Q}[x]/(x^{11} - \cdots)$$ None $$-4$$ $$-8$$ $$11$$ $$-9$$ $$-$$ $$-$$ $$q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots$$
1205.2.a.c $$15$$ $$9.622$$ $$\mathbb{Q}[x]/(x^{15} - \cdots)$$ None $$2$$ $$-7$$ $$-15$$ $$-3$$ $$+$$ $$+$$ $$q+\beta _{1}q^{2}+\beta _{11}q^{3}+\beta _{2}q^{4}-q^{5}+(-\beta _{8}+\cdots)q^{6}+\cdots$$
1205.2.a.d $$25$$ $$9.622$$ None $$-4$$ $$9$$ $$-25$$ $$7$$ $$+$$ $$-$$
1205.2.a.e $$25$$ $$9.622$$ None $$6$$ $$15$$ $$25$$ $$19$$ $$-$$ $$+$$

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_0(1205))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_0(1205)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_0(241))$$$$^{\oplus 2}$$