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 $3$

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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

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

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

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