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 $2$

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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

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