Properties

Label 2645.2.a
Level $2645$
Weight $2$
Character orbit 2645.a
Rep. character $\chi_{2645}(1,\cdot)$
Character field $\Q$
Dimension $169$
Newform subspaces $25$
Sturm bound $552$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2645 = 5 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2645.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 25 \)
Sturm bound: \(552\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2645))\).

Total New Old
Modular forms 300 169 131
Cusp forms 253 169 84
Eisenstein series 47 0 47

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

\(5\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(37\)
\(+\)\(-\)\(-\)\(48\)
\(-\)\(+\)\(-\)\(47\)
\(-\)\(-\)\(+\)\(37\)
Plus space\(+\)\(74\)
Minus space\(-\)\(95\)

Trace form

\( 169q - q^{2} + 4q^{3} + 167q^{4} - q^{5} - 8q^{6} + 4q^{7} - 9q^{8} + 177q^{9} + O(q^{10}) \) \( 169q - q^{2} + 4q^{3} + 167q^{4} - q^{5} - 8q^{6} + 4q^{7} - 9q^{8} + 177q^{9} - 3q^{10} - 4q^{11} + 16q^{12} + 10q^{13} + 12q^{14} + 159q^{16} + 2q^{17} - 9q^{18} + 4q^{19} + q^{20} - 12q^{21} + 8q^{22} + 12q^{24} + 169q^{25} - 18q^{26} - 8q^{27} + 8q^{28} - 18q^{29} + 4q^{30} - 9q^{32} + 10q^{34} + 159q^{36} - 2q^{37} - 28q^{38} - 20q^{39} - 15q^{40} - 10q^{41} - 8q^{42} + 12q^{43} + 32q^{44} - 13q^{45} - 16q^{47} + 16q^{48} + 173q^{49} - q^{50} + 4q^{51} + 14q^{52} - 18q^{53} + 4q^{54} - 4q^{55} + 24q^{56} - 58q^{58} - 24q^{59} + 16q^{60} + 6q^{61} + 28q^{62} + 12q^{63} + 135q^{64} - 10q^{65} - 36q^{66} - 8q^{67} - 26q^{68} + 12q^{70} + 4q^{71} - 81q^{72} + 26q^{73} - 34q^{74} + 4q^{75} + 28q^{76} - 12q^{77} - 32q^{78} - 12q^{79} + q^{80} + 193q^{81} - 34q^{82} + 16q^{83} - 16q^{84} - 2q^{85} + 8q^{86} - 4q^{87} - 12q^{88} - 14q^{89} - 3q^{90} + 44q^{91} - 12q^{93} - 40q^{94} + 4q^{95} + 16q^{96} + 22q^{97} - 17q^{98} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2645))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 23
2645.2.a.a \(1\) \(21.120\) \(\Q\) None \(0\) \(-2\) \(-1\) \(3\) \(+\) \(-\) \(q-2q^{3}-2q^{4}-q^{5}+3q^{7}+q^{9}+6q^{11}+\cdots\)
2645.2.a.b \(1\) \(21.120\) \(\Q\) None \(0\) \(-2\) \(1\) \(-3\) \(-\) \(-\) \(q-2q^{3}-2q^{4}+q^{5}-3q^{7}+q^{9}-6q^{11}+\cdots\)
2645.2.a.c \(1\) \(21.120\) \(\Q\) None \(2\) \(0\) \(1\) \(-1\) \(-\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}-q^{7}-3q^{9}+2q^{10}+\cdots\)
2645.2.a.d \(2\) \(21.120\) \(\Q(\sqrt{5}) \) None \(-3\) \(-2\) \(2\) \(2\) \(-\) \(-\) \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+q^{5}+\cdots\)
2645.2.a.e \(2\) \(21.120\) \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(-2\) \(4\) \(+\) \(-\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(2-2\beta )q^{4}+\cdots\)
2645.2.a.f \(2\) \(21.120\) \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(2\) \(-4\) \(-\) \(-\) \(q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(2-2\beta )q^{4}+\cdots\)
2645.2.a.g \(2\) \(21.120\) \(\Q(\sqrt{13}) \) None \(-1\) \(2\) \(-2\) \(2\) \(+\) \(-\) \(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
2645.2.a.h \(2\) \(21.120\) \(\Q(\sqrt{13}) \) None \(-1\) \(2\) \(2\) \(-2\) \(-\) \(-\) \(q-\beta q^{2}+q^{3}+(1+\beta )q^{4}+q^{5}-\beta q^{6}+\cdots\)
2645.2.a.i \(4\) \(21.120\) 4.4.65057.1 None \(-1\) \(-1\) \(-4\) \(7\) \(+\) \(-\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
2645.2.a.j \(4\) \(21.120\) 4.4.65057.1 None \(-1\) \(-1\) \(4\) \(-7\) \(-\) \(-\) \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
2645.2.a.k \(4\) \(21.120\) 4.4.2777.1 None \(-1\) \(1\) \(-4\) \(3\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
2645.2.a.l \(4\) \(21.120\) 4.4.2777.1 None \(-1\) \(1\) \(4\) \(-3\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(\beta _{1}-\beta _{2})q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
2645.2.a.m \(4\) \(21.120\) 4.4.15317.1 None \(2\) \(-2\) \(-4\) \(3\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2645.2.a.n \(5\) \(21.120\) \(\Q(\zeta_{22})^+\) None \(-3\) \(-5\) \(-5\) \(-3\) \(+\) \(+\) \(q+(-1+\beta _{1}-\beta _{4})q^{2}-q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
2645.2.a.o \(5\) \(21.120\) \(\Q(\zeta_{22})^+\) None \(-3\) \(-5\) \(5\) \(3\) \(-\) \(-\) \(q+(-1+\beta _{1}-\beta _{4})q^{2}-q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
2645.2.a.p \(6\) \(21.120\) 6.6.27387072.1 None \(0\) \(-6\) \(-6\) \(6\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(1+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
2645.2.a.q \(6\) \(21.120\) 6.6.27387072.1 None \(0\) \(-6\) \(6\) \(-6\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(1+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
2645.2.a.r \(6\) \(21.120\) 6.6.4829696.1 None \(2\) \(4\) \(-6\) \(-6\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
2645.2.a.s \(6\) \(21.120\) 6.6.4829696.1 None \(2\) \(4\) \(6\) \(6\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
2645.2.a.t \(10\) \(21.120\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-5\) \(-10\) \(9\) \(+\) \(+\) \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-\beta _{7}q^{4}-q^{5}+\beta _{3}q^{6}+\cdots\)
2645.2.a.u \(10\) \(21.120\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-5\) \(10\) \(-9\) \(-\) \(-\) \(q-\beta _{2}q^{2}+(-1+\beta _{1})q^{3}-\beta _{7}q^{4}+q^{5}+\cdots\)
2645.2.a.v \(16\) \(21.120\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(4\) \(-16\) \(-12\) \(+\) \(+\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
2645.2.a.w \(16\) \(21.120\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(4\) \(16\) \(12\) \(-\) \(+\) \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
2645.2.a.x \(25\) \(21.120\) None \(3\) \(10\) \(-25\) \(-14\) \(+\) \(-\)
2645.2.a.y \(25\) \(21.120\) None \(3\) \(10\) \(25\) \(14\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2645))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2645)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 2}\)