Properties

Label 1205.2.a
Level 1205
Weight 2
Character orbit a
Rep. character \(\chi_{1205}(1,\cdot)\)
Character field \(\Q\)
Dimension 81
Newforms 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: \(\Q\)
Newforms: \( 5 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1205))\) into irreducible Hecke orbits

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

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