Properties

Label 150.2.a
Level 150
Weight 2
Character orbit a
Rep. character \(\chi_{150}(1,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 3
Sturm bound 60
Trace bound 3

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 150.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(150))\).

Total New Old
Modular forms 42 3 39
Cusp forms 19 3 16
Eisenstein series 23 0 23

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

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(3\)

Trace form

\(3q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 3q^{4} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 3q^{4} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 3q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut -\mathstrut 14q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut -\mathstrut 10q^{34} \) \(\mathstrut +\mathstrut 3q^{36} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 10q^{39} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 8q^{46} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 3q^{49} \) \(\mathstrut +\mathstrut 2q^{51} \) \(\mathstrut -\mathstrut 2q^{52} \) \(\mathstrut +\mathstrut 6q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut +\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 6q^{58} \) \(\mathstrut +\mathstrut 20q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 8q^{62} \) \(\mathstrut +\mathstrut 4q^{63} \) \(\mathstrut +\mathstrut 3q^{64} \) \(\mathstrut +\mathstrut 4q^{66} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 6q^{68} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut +\mathstrut 24q^{71} \) \(\mathstrut +\mathstrut q^{72} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut -\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut 2q^{78} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 3q^{81} \) \(\mathstrut -\mathstrut 6q^{82} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 12q^{86} \) \(\mathstrut +\mathstrut 6q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut -\mathstrut 8q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut 9q^{98} \) \(\mathstrut +\mathstrut 4q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(150))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5
150.2.a.a \(1\) \(1.198\) \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q-q^{2}-q^{3}+q^{4}+q^{6}+2q^{7}-q^{8}+\cdots\)
150.2.a.b \(1\) \(1.198\) \(\Q\) None \(1\) \(-1\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+4q^{7}+q^{8}+\cdots\)
150.2.a.c \(1\) \(1.198\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(150))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(150)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)