Properties

Label 345.2.a
Level $345$
Weight $2$
Character orbit 345.a
Rep. character $\chi_{345}(1,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $10$
Sturm bound $96$
Trace bound $3$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 345 = 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 345.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(345))\).

Total New Old
Modular forms 52 15 37
Cusp forms 45 15 30
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.

\(3\)\(5\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(9\)

Trace form

\( 15q - 3q^{2} + 3q^{3} + 13q^{4} - q^{5} - 3q^{6} - 15q^{8} + 15q^{9} + O(q^{10}) \) \( 15q - 3q^{2} + 3q^{3} + 13q^{4} - q^{5} - 3q^{6} - 15q^{8} + 15q^{9} - 3q^{10} - 12q^{11} + 5q^{12} + 10q^{13} + 8q^{14} - q^{15} + 13q^{16} - 2q^{17} - 3q^{18} - 12q^{19} + 9q^{20} + 8q^{21} + 4q^{22} - q^{23} + 9q^{24} + 15q^{25} - 26q^{26} + 3q^{27} - 8q^{28} - 10q^{29} - 3q^{30} - 12q^{31} - 23q^{32} - 4q^{33} + 26q^{34} - 4q^{35} + 13q^{36} - 6q^{37} - 4q^{38} + 2q^{39} - 15q^{40} - 30q^{41} - 12q^{43} - 28q^{44} - q^{45} - 3q^{46} - 24q^{47} - 3q^{48} + 35q^{49} - 3q^{50} - 10q^{51} + 30q^{52} + 18q^{53} - 3q^{54} + 4q^{55} + 32q^{56} + 20q^{57} - 26q^{58} + 8q^{59} - 7q^{60} + 18q^{61} + 32q^{62} - 3q^{64} - 14q^{65} - 12q^{66} - 20q^{67} - 22q^{68} - q^{69} + 24q^{70} - 12q^{71} - 15q^{72} - 18q^{73} - 10q^{74} + 3q^{75} + 4q^{76} + 40q^{77} + 30q^{78} - 8q^{79} + q^{80} + 15q^{81} - 22q^{82} - 4q^{83} + 8q^{84} - 6q^{85} + 4q^{86} + 18q^{87} - 4q^{88} - 2q^{89} - 3q^{90} + 32q^{91} - 7q^{92} + 16q^{93} - 16q^{94} - 4q^{95} + 25q^{96} - 2q^{97} - 51q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(345))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 23
345.2.a.a \(1\) \(2.755\) \(\Q\) None \(-2\) \(1\) \(1\) \(-5\) \(-\) \(-\) \(+\) \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-5q^{7}+\cdots\)
345.2.a.b \(1\) \(2.755\) \(\Q\) None \(-1\) \(1\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
345.2.a.c \(1\) \(2.755\) \(\Q\) None \(0\) \(-1\) \(-1\) \(1\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{4}-q^{5}+q^{7}+q^{9}+4q^{11}+\cdots\)
345.2.a.d \(1\) \(2.755\) \(\Q\) None \(0\) \(1\) \(-1\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{4}-q^{5}-3q^{7}+q^{9}-4q^{11}+\cdots\)
345.2.a.e \(1\) \(2.755\) \(\Q\) None \(1\) \(1\) \(-1\) \(4\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}+4q^{7}+\cdots\)
345.2.a.f \(1\) \(2.755\) \(\Q\) None \(2\) \(-1\) \(1\) \(3\) \(+\) \(-\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
345.2.a.g \(2\) \(2.755\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(-6\) \(+\) \(-\) \(-\) \(q+(-1+\beta )q^{2}-q^{3}+(2-2\beta )q^{4}+q^{5}+\cdots\)
345.2.a.h \(2\) \(2.755\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(+\) \(q+\beta q^{2}-q^{3}-q^{5}-\beta q^{6}+(-1-2\beta )q^{7}+\cdots\)
345.2.a.i \(2\) \(2.755\) \(\Q(\sqrt{6}) \) None \(0\) \(2\) \(-2\) \(-2\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+q^{3}+4q^{4}-q^{5}+\beta q^{6}-q^{7}+\cdots\)
345.2.a.j \(3\) \(2.755\) 3.3.316.1 None \(-1\) \(3\) \(3\) \(6\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(345))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(345)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 2}\)