Properties

Label 275.2.a
Level $275$
Weight $2$
Character orbit 275.a
Rep. character $\chi_{275}(1,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $8$
Sturm bound $60$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 275 = 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 275.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(60\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(275))\).

Total New Old
Modular forms 36 16 20
Cusp forms 25 16 9
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.

\(5\)\(11\)FrickeDim.
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(5\)
Minus space\(-\)\(11\)

Trace form

\( 16 q - q^{2} + q^{3} + 13 q^{4} - 2 q^{6} + 6 q^{7} - 3 q^{8} + 11 q^{9} + O(q^{10}) \) \( 16 q - q^{2} + q^{3} + 13 q^{4} - 2 q^{6} + 6 q^{7} - 3 q^{8} + 11 q^{9} - 2 q^{11} + 18 q^{12} + 2 q^{13} - 8 q^{14} + 3 q^{16} - 12 q^{17} - 11 q^{18} + 8 q^{19} - 6 q^{21} + q^{22} - 3 q^{23} - 16 q^{24} + 22 q^{26} - 5 q^{27} + 8 q^{28} - 6 q^{29} + q^{31} - 7 q^{32} + q^{33} - 30 q^{34} - 17 q^{36} + 3 q^{37} + 4 q^{38} + 24 q^{39} - 2 q^{41} - 12 q^{42} + 14 q^{43} - 9 q^{44} - 30 q^{46} + 4 q^{47} - 4 q^{48} + 32 q^{49} - 2 q^{51} - 14 q^{52} - 4 q^{53} - 6 q^{54} - 12 q^{56} + 6 q^{58} - 25 q^{59} - 6 q^{61} + 22 q^{62} + 16 q^{63} - 13 q^{64} + 6 q^{66} + 15 q^{67} - 14 q^{68} - 37 q^{69} - 9 q^{71} - 39 q^{72} - 10 q^{73} + 24 q^{74} - 8 q^{76} + 6 q^{77} - 24 q^{78} + 22 q^{79} - 20 q^{81} - 30 q^{82} + 22 q^{83} - 64 q^{84} - 72 q^{86} - 32 q^{87} - 9 q^{88} - 21 q^{89} + 36 q^{91} + 22 q^{92} + 7 q^{93} + 64 q^{94} + 4 q^{96} + q^{97} + 7 q^{98} + 9 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(275))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 11
275.2.a.a \(1\) \(2.196\) \(\Q\) None \(-1\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q-q^{2}-q^{4}+3q^{8}-3q^{9}-q^{11}-2q^{13}+\cdots\)
275.2.a.b \(1\) \(2.196\) \(\Q\) None \(2\) \(1\) \(0\) \(2\) \(+\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+2q^{7}+\cdots\)
275.2.a.c \(2\) \(2.196\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(4\) \(+\) \(-\) \(q+(-1+\beta )q^{2}-2\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
275.2.a.d \(2\) \(2.196\) \(\Q(\sqrt{5}) \) None \(-1\) \(-3\) \(0\) \(-1\) \(-\) \(-\) \(q-\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
275.2.a.e \(2\) \(2.196\) \(\Q(\sqrt{13}) \) None \(-1\) \(-1\) \(0\) \(-5\) \(+\) \(+\) \(q-\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}-3q^{6}+\cdots\)
275.2.a.f \(2\) \(2.196\) \(\Q(\sqrt{13}) \) None \(1\) \(1\) \(0\) \(5\) \(-\) \(+\) \(q+\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}-3q^{6}+\cdots\)
275.2.a.g \(2\) \(2.196\) \(\Q(\sqrt{5}) \) None \(1\) \(3\) \(0\) \(1\) \(+\) \(-\) \(q+\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{6}+\cdots\)
275.2.a.h \(4\) \(2.196\) \(\Q(\sqrt{3}, \sqrt{11})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(2+\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(275))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(275)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 2}\)