Properties

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

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Defining parameters

Level: \( N \) = \( 236 = 2^{2} \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 236.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(236))\) into newform subspaces

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

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