Properties

Label 200.2.a
Level 200
Weight 2
Character orbit a
Rep. character \(\chi_{200}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 5
Sturm bound 60
Trace bound 3

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Defining parameters

Level: \( N \) = \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 200.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(200))\).

Total New Old
Modular forms 42 5 37
Cusp forms 19 5 14
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.

\(2\)\(5\)FrickeDim.
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(4\)

Trace form

\(5q \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 11q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 11q^{9} \) \(\mathstrut -\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 12q^{31} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut -\mathstrut 8q^{39} \) \(\mathstrut -\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 3q^{49} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 6q^{53} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 2q^{61} \) \(\mathstrut -\mathstrut 12q^{63} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 16q^{77} \) \(\mathstrut +\mathstrut 44q^{79} \) \(\mathstrut +\mathstrut 5q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 12q^{89} \) \(\mathstrut +\mathstrut 40q^{91} \) \(\mathstrut +\mathstrut 14q^{97} \) \(\mathstrut -\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(200))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
200.2.a.a \(1\) \(1.597\) \(\Q\) None \(0\) \(-3\) \(0\) \(2\) \(+\) \(-\) \(q-3q^{3}+2q^{7}+6q^{9}+q^{11}+4q^{13}+\cdots\)
200.2.a.b \(1\) \(1.597\) \(\Q\) None \(0\) \(-2\) \(0\) \(-2\) \(-\) \(-\) \(q-2q^{3}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots\)
200.2.a.c \(1\) \(1.597\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(q+4q^{7}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
200.2.a.d \(1\) \(1.597\) \(\Q\) None \(0\) \(2\) \(0\) \(2\) \(+\) \(-\) \(q+2q^{3}+2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
200.2.a.e \(1\) \(1.597\) \(\Q\) None \(0\) \(3\) \(0\) \(-2\) \(-\) \(+\) \(q+3q^{3}-2q^{7}+6q^{9}+q^{11}-4q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(200))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(200)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)