Properties

Label 825.2.a
Level $825$
Weight $2$
Character orbit 825.a
Rep. character $\chi_{825}(1,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $14$
Sturm bound $240$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(240\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(825))\).

Total New Old
Modular forms 132 32 100
Cusp forms 109 32 77
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.

\(3\)\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(11\)
Minus space\(-\)\(21\)

Trace form

\( 32q + 2q^{2} - 2q^{3} + 36q^{4} + 4q^{6} - 4q^{7} + 18q^{8} + 32q^{9} + O(q^{10}) \) \( 32q + 2q^{2} - 2q^{3} + 36q^{4} + 4q^{6} - 4q^{7} + 18q^{8} + 32q^{9} - 6q^{12} + 20q^{14} + 52q^{16} + 12q^{17} + 2q^{18} - 8q^{19} - 16q^{21} - 2q^{22} + 12q^{24} - 44q^{26} - 2q^{27} - 4q^{28} - 12q^{29} + 12q^{31} + 18q^{32} - 2q^{33} + 8q^{34} + 36q^{36} - 16q^{37} - 4q^{38} - 16q^{39} - 20q^{41} + 12q^{42} + 4q^{43} + 8q^{44} - 8q^{46} + 8q^{47} + 2q^{48} + 12q^{49} + 56q^{52} + 16q^{53} + 4q^{54} + 36q^{56} - 20q^{57} + 32q^{59} - 20q^{61} - 32q^{62} - 4q^{63} + 76q^{64} + 4q^{66} - 8q^{67} - 52q^{68} + 16q^{69} + 24q^{71} + 18q^{72} + 24q^{73} + 4q^{74} - 20q^{76} - 4q^{77} + 16q^{78} - 4q^{79} + 32q^{81} - 16q^{83} - 36q^{84} + 20q^{86} + 6q^{88} + 16q^{89} - 4q^{91} - 8q^{93} - 64q^{94} - 12q^{96} - 16q^{97} - 70q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(825))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 11
825.2.a.a \(1\) \(6.588\) \(\Q\) None \(-1\) \(1\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{3}-q^{4}-q^{6}-4q^{7}+3q^{8}+\cdots\)
825.2.a.b \(1\) \(6.588\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{4}+q^{7}+q^{9}-q^{11}+2q^{12}+\cdots\)
825.2.a.c \(1\) \(6.588\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q+q^{3}-2q^{4}-q^{7}+q^{9}-q^{11}-2q^{12}+\cdots\)
825.2.a.d \(2\) \(6.588\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(1+\cdots)q^{6}+\cdots\)
825.2.a.e \(2\) \(6.588\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}-2q^{7}-\beta q^{8}+\cdots\)
825.2.a.f \(2\) \(6.588\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(1+\beta )q^{6}+\cdots\)
825.2.a.g \(2\) \(6.588\) \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+(1+\beta )q^{6}+\cdots\)
825.2.a.h \(3\) \(6.588\) 3.3.148.1 None \(-3\) \(3\) \(0\) \(-8\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
825.2.a.i \(3\) \(6.588\) 3.3.568.1 None \(-2\) \(-3\) \(0\) \(3\) \(+\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}-q^{3}+(3+\beta _{2})q^{4}+\cdots\)
825.2.a.j \(3\) \(6.588\) 3.3.148.1 None \(-1\) \(-3\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
825.2.a.k \(3\) \(6.588\) 3.3.148.1 None \(1\) \(-3\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
825.2.a.l \(3\) \(6.588\) 3.3.148.1 None \(1\) \(3\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
825.2.a.m \(3\) \(6.588\) 3.3.568.1 None \(2\) \(3\) \(0\) \(-3\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+q^{3}+(3+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
825.2.a.n \(3\) \(6.588\) 3.3.148.1 None \(3\) \(-3\) \(0\) \(8\) \(+\) \(-\) \(+\) \(q+(1+\beta _{2})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(825))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(825)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 2}\)