Properties

Label 236.2.a
Level 236
Weight 2
Character orbit a
Rep. character \(\chi_{236}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 3
Sturm bound 60
Trace bound 3

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 236 = 2^{2} \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 236.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(236))\).

Total New Old
Modular forms 33 5 28
Cusp forms 28 5 23
Eisenstein series 5 0 5

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

\(2\)\(59\)FrickeDim.
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(4\)

Trace form

\(5q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 9q^{21} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 10q^{39} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 20q^{43} \) \(\mathstrut -\mathstrut 35q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 14q^{53} \) \(\mathstrut -\mathstrut 19q^{57} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 10q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 12q^{67} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 23q^{71} \) \(\mathstrut +\mathstrut 8q^{73} \) \(\mathstrut -\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 29q^{81} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 24q^{85} \) \(\mathstrut -\mathstrut 21q^{87} \) \(\mathstrut -\mathstrut 14q^{89} \) \(\mathstrut +\mathstrut 18q^{91} \) \(\mathstrut +\mathstrut 22q^{93} \) \(\mathstrut +\mathstrut 4q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(236))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 59
236.2.a.a \(1\) \(1.884\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-3\) \(-\) \(-\) \(q-q^{3}-q^{5}-3q^{7}-2q^{9}-2q^{11}+\cdots\)
236.2.a.b \(1\) \(1.884\) \(\Q\) None \(0\) \(1\) \(3\) \(-1\) \(-\) \(+\) \(q+q^{3}+3q^{5}-q^{7}-2q^{9}+6q^{11}+\cdots\)
236.2.a.c \(3\) \(1.884\) 3.3.321.1 None \(0\) \(0\) \(-4\) \(8\) \(-\) \(+\) \(q+(-\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{1})q^{5}+(3+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(236))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(236)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(118))\)\(^{\oplus 2}\)