Properties

Label 364.2.a
Level 364
Weight 2
Character orbit a
Rep. character \(\chi_{364}(1,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 4
Sturm bound 112
Trace bound 3

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Defining parameters

Level: \( N \) = \( 364 = 2^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 364.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(112\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(364))\).

Total New Old
Modular forms 62 6 56
Cusp forms 51 6 45
Eisenstein series 11 0 11

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

\(2\)\(7\)\(13\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(4\)

Trace form

\(6q \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 4q^{15} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 12q^{27} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 20q^{31} \) \(\mathstrut -\mathstrut 4q^{33} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 8q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 8q^{45} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut +\mathstrut 16q^{51} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut -\mathstrut 8q^{63} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut -\mathstrut 12q^{67} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 20q^{75} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut -\mathstrut 18q^{81} \) \(\mathstrut -\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 16q^{87} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut +\mathstrut 2q^{91} \) \(\mathstrut -\mathstrut 20q^{93} \) \(\mathstrut +\mathstrut 26q^{95} \) \(\mathstrut -\mathstrut 24q^{97} \) \(\mathstrut +\mathstrut 20q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(364))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 13
364.2.a.a \(1\) \(2.907\) \(\Q\) None \(0\) \(-2\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(q-2q^{3}+q^{5}-q^{7}+q^{9}-4q^{11}+q^{13}+\cdots\)
364.2.a.b \(1\) \(2.907\) \(\Q\) None \(0\) \(0\) \(-3\) \(1\) \(-\) \(-\) \(+\) \(q-3q^{5}+q^{7}-3q^{9}-2q^{11}-q^{13}+\cdots\)
364.2.a.c \(2\) \(2.907\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta q^{3}+(-1+\beta )q^{5}-q^{7}+3q^{9}+\cdots\)
364.2.a.d \(2\) \(2.907\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{3}-\beta q^{5}+q^{7}+(1+2\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(364))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(364)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 2}\)