Properties

Label 801.2.a
Level 801
Weight 2
Character orbit a
Rep. character \(\chi_{801}(1,\cdot)\)
Character field \(\Q\)
Dimension 36
Newforms 11
Sturm bound 180
Trace bound 5

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Defining parameters

Level: \( N \) = \( 801 = 3^{2} \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 801.a (trivial)
Character field: \(\Q\)
Newforms: \( 11 \)
Sturm bound: \(180\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(801))\).

Total New Old
Modular forms 94 36 58
Cusp forms 87 36 51
Eisenstein series 7 0 7

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

\(3\)\(89\)FrickeDim.
\(+\)\(+\)\(+\)\(7\)
\(+\)\(-\)\(-\)\(7\)
\(-\)\(+\)\(-\)\(14\)
\(-\)\(-\)\(+\)\(8\)
Plus space\(+\)\(15\)
Minus space\(-\)\(21\)

Trace form

\(36q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(36q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut 14q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 18q^{25} \) \(\mathstrut -\mathstrut 18q^{26} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut -\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 8q^{43} \) \(\mathstrut +\mathstrut 32q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut -\mathstrut 28q^{50} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut +\mathstrut 34q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 38q^{58} \) \(\mathstrut -\mathstrut 10q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut +\mathstrut 32q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 20q^{67} \) \(\mathstrut +\mathstrut 2q^{68} \) \(\mathstrut -\mathstrut 34q^{70} \) \(\mathstrut -\mathstrut 12q^{71} \) \(\mathstrut -\mathstrut 18q^{73} \) \(\mathstrut -\mathstrut 12q^{74} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut +\mathstrut 28q^{77} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 42q^{80} \) \(\mathstrut -\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 52q^{86} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut -\mathstrut 44q^{92} \) \(\mathstrut -\mathstrut 28q^{94} \) \(\mathstrut -\mathstrut 50q^{95} \) \(\mathstrut -\mathstrut 46q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(801))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 89
801.2.a.a \(1\) \(6.396\) \(\Q\) None \(-1\) \(0\) \(2\) \(2\) \(-\) \(+\) \(q-q^{2}-q^{4}+2q^{5}+2q^{7}+3q^{8}-2q^{10}+\cdots\)
801.2.a.b \(1\) \(6.396\) \(\Q\) None \(0\) \(0\) \(-4\) \(-2\) \(-\) \(+\) \(q-2q^{4}-4q^{5}-2q^{7}-2q^{11}+6q^{13}+\cdots\)
801.2.a.c \(1\) \(6.396\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(q-2q^{4}+2q^{7}-6q^{11}+2q^{13}+4q^{16}+\cdots\)
801.2.a.d \(1\) \(6.396\) \(\Q\) None \(1\) \(0\) \(1\) \(-4\) \(-\) \(-\) \(q+q^{2}-q^{4}+q^{5}-4q^{7}-3q^{8}+q^{10}+\cdots\)
801.2.a.e \(3\) \(6.396\) 3.3.169.1 None \(-2\) \(0\) \(-5\) \(-4\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
801.2.a.f \(3\) \(6.396\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(3\) \(-6\) \(-\) \(-\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
801.2.a.g \(3\) \(6.396\) \(\Q(\zeta_{14})^+\) None \(4\) \(0\) \(7\) \(-4\) \(-\) \(+\) \(q+(1+\beta _{1})q^{2}+(1+2\beta _{1}+\beta _{2})q^{4}+(2+\cdots)q^{5}+\cdots\)
801.2.a.h \(4\) \(6.396\) 4.4.23377.1 None \(-1\) \(0\) \(-3\) \(6\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
801.2.a.i \(5\) \(6.396\) 5.5.535120.1 None \(1\) \(0\) \(1\) \(8\) \(-\) \(+\) \(q+\beta _{2}q^{2}+(3-\beta _{1}+\beta _{3})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
801.2.a.j \(7\) \(6.396\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-4\) \(0\) \(-4\) \(0\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
801.2.a.k \(7\) \(6.396\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4\) \(0\) \(4\) \(0\) \(+\) \(-\) \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(801))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(801)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(267))\)\(^{\oplus 2}\)