Properties

Label 333.2.a
Level $333$
Weight $2$
Character orbit 333.a
Rep. character $\chi_{333}(1,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $7$
Sturm bound $76$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 333 = 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 333.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(76\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(333))\).

Total New Old
Modular forms 42 15 27
Cusp forms 35 15 20
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.

\(3\)\(37\)FrickeDim
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(6\)
Minus space\(-\)\(9\)

Trace form

\( 15 q - q^{2} + 11 q^{4} - 2 q^{7} - 3 q^{8} + O(q^{10}) \) \( 15 q - q^{2} + 11 q^{4} - 2 q^{7} - 3 q^{8} - 10 q^{10} - 2 q^{11} + 10 q^{14} + 3 q^{16} - 8 q^{17} - 2 q^{19} + 26 q^{20} - 2 q^{22} + 4 q^{23} + 5 q^{25} + 18 q^{26} - 8 q^{28} - 14 q^{29} - 7 q^{32} - 2 q^{34} + 2 q^{35} + q^{37} - 8 q^{38} - 22 q^{40} - 12 q^{41} - 10 q^{43} - 20 q^{44} + 4 q^{46} + 22 q^{47} + 25 q^{49} - 27 q^{50} - 2 q^{52} - 14 q^{55} + 32 q^{56} - 10 q^{58} - 16 q^{59} + 14 q^{61} - 12 q^{62} + 11 q^{64} - 40 q^{65} - 16 q^{67} - 38 q^{68} + 20 q^{70} + 6 q^{71} - 20 q^{73} - 5 q^{74} + 30 q^{77} + 26 q^{79} + 30 q^{80} + 8 q^{82} + 26 q^{83} - 12 q^{85} - 20 q^{86} - 20 q^{88} - 32 q^{89} - 2 q^{91} + 48 q^{92} - 30 q^{94} + 56 q^{95} - 2 q^{97} - 87 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(333))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 37
333.2.a.a 333.a 1.a $1$ $2.659$ \(\Q\) None 333.2.a.a \(-1\) \(0\) \(2\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}-4q^{7}+3q^{8}-2q^{10}+\cdots\)
333.2.a.b 333.a 1.a $1$ $2.659$ \(\Q\) None 37.2.a.b \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{7}-3q^{11}-4q^{13}+4q^{16}+\cdots\)
333.2.a.c 333.a 1.a $1$ $2.659$ \(\Q\) None 333.2.a.a \(1\) \(0\) \(-2\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{5}-4q^{7}-3q^{8}-2q^{10}+\cdots\)
333.2.a.d 333.a 1.a $1$ $2.659$ \(\Q\) None 37.2.a.a \(2\) \(0\) \(2\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+2q^{5}-q^{7}+4q^{10}+\cdots\)
333.2.a.e 333.a 1.a $3$ $2.659$ 3.3.148.1 None 111.2.a.a \(-3\) \(0\) \(-4\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
333.2.a.f 333.a 1.a $4$ $2.659$ 4.4.27648.1 None 333.2.a.f \(0\) \(0\) \(0\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+2q^{7}+\cdots\)
333.2.a.g 333.a 1.a $4$ $2.659$ 4.4.6224.1 None 111.2.a.b \(0\) \(0\) \(2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(333))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(333)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 2}\)