Properties

Label 207.2.a
Level $207$
Weight $2$
Character orbit 207.a
Rep. character $\chi_{207}(1,\cdot)$
Character field $\Q$
Dimension $9$
Newform subspaces $5$
Sturm bound $48$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 207 = 3^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 207.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(48\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(207))\).

Total New Old
Modular forms 28 9 19
Cusp forms 21 9 12
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.

\(3\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(3\)
Minus space\(-\)\(6\)

Trace form

\( 9q + 8q^{4} + 4q^{5} - 6q^{7} + 3q^{8} + O(q^{10}) \) \( 9q + 8q^{4} + 4q^{5} - 6q^{7} + 3q^{8} - 4q^{10} - 6q^{11} + 8q^{14} + 6q^{16} + 10q^{20} - 14q^{22} - 3q^{23} + 3q^{25} - 11q^{26} - 22q^{28} + 4q^{29} - 14q^{32} + 18q^{34} - 16q^{35} - 4q^{37} + 6q^{38} - 4q^{40} - 12q^{43} - 28q^{44} + 2q^{46} + 8q^{47} - 11q^{49} - 4q^{50} + 3q^{52} + 26q^{53} + 4q^{55} + 14q^{56} + 33q^{58} + 6q^{61} - 39q^{62} - 43q^{64} + 26q^{65} + 26q^{67} + 32q^{68} - 12q^{70} - 12q^{71} + 12q^{73} + 24q^{74} - 26q^{76} + 16q^{77} + 4q^{79} - 20q^{80} + 15q^{82} + 2q^{83} + 44q^{85} - 40q^{86} - 18q^{88} + 26q^{89} - 2q^{91} - 6q^{92} + 3q^{94} - 4q^{95} - 20q^{97} + 12q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(207))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 23
207.2.a.a \(1\) \(1.653\) \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(q-q^{2}-q^{4}-2q^{7}+3q^{8}-4q^{11}+\cdots\)
207.2.a.b \(2\) \(1.653\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-4\) \(-4\) \(+\) \(+\) \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-2-\beta )q^{5}+\cdots\)
207.2.a.c \(2\) \(1.653\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(2\) \(-\) \(+\) \(q-\beta q^{2}+3q^{4}+(1+\beta )q^{5}+(1-\beta )q^{7}+\cdots\)
207.2.a.d \(2\) \(1.653\) \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(2\) \(2\) \(-\) \(+\) \(q+\beta q^{2}+(-1+\beta )q^{4}+2\beta q^{5}+(2-2\beta )q^{7}+\cdots\)
207.2.a.e \(2\) \(1.653\) \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(4\) \(-4\) \(+\) \(-\) \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(2-\beta )q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(207))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(207)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 2}\)