Properties

Label 212.2.a
Level 212
Weight 2
Character orbit a
Rep. character \(\chi_{212}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 3
Sturm bound 54
Trace bound 3

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Defining parameters

Level: \( N \) = \( 212 = 2^{2} \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 212.a (trivial)
Character field: \(\Q\)
Newforms: \( 3 \)
Sturm bound: \(54\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(212))\).

Total New Old
Modular forms 30 5 25
Cusp forms 25 5 20
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.

\(2\)\(53\)FrickeDim.
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(4\)

Trace form

\(5q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 5q^{9} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 2q^{21} \) \(\mathstrut -\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut -\mathstrut 14q^{27} \) \(\mathstrut +\mathstrut 2q^{29} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut -\mathstrut 20q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 2q^{41} \) \(\mathstrut -\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 5q^{49} \) \(\mathstrut -\mathstrut 20q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 28q^{57} \) \(\mathstrut -\mathstrut 20q^{59} \) \(\mathstrut +\mathstrut 28q^{63} \) \(\mathstrut +\mathstrut 10q^{65} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 16q^{69} \) \(\mathstrut -\mathstrut 6q^{71} \) \(\mathstrut +\mathstrut 28q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 18q^{79} \) \(\mathstrut +\mathstrut 5q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut +\mathstrut 22q^{85} \) \(\mathstrut +\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 26q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 48q^{93} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 44q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(212))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 53
212.2.a.a \(1\) \(1.693\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-2\) \(-\) \(-\) \(q-q^{3}-2q^{5}-2q^{7}-2q^{9}+2q^{11}+\cdots\)
212.2.a.b \(1\) \(1.693\) \(\Q\) None \(0\) \(2\) \(2\) \(0\) \(-\) \(+\) \(q+2q^{3}+2q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
212.2.a.c \(3\) \(1.693\) 3.3.756.1 None \(0\) \(-3\) \(0\) \(6\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{3}-\beta _{2}q^{5}+(2+\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(212))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(212)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(53))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(106))\)\(^{\oplus 2}\)