Properties

Label 184.2.a
Level $184$
Weight $2$
Character orbit 184.a
Rep. character $\chi_{184}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $5$
Sturm bound $48$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 184.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(48\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(184))\).

Total New Old
Modular forms 28 6 22
Cusp forms 21 6 15
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.

\(2\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(4\)

Trace form

\( 6q - 2q^{5} + 2q^{9} + O(q^{10}) \) \( 6q - 2q^{5} + 2q^{9} + 2q^{11} + 4q^{15} - 4q^{17} + 2q^{19} - 4q^{21} - 2q^{25} + 12q^{27} + 12q^{29} - 12q^{31} - 12q^{33} - 18q^{37} - 28q^{39} + 4q^{41} - 10q^{43} + 18q^{45} + 4q^{47} - 2q^{49} + 4q^{51} - 6q^{53} + 24q^{55} - 26q^{61} - 20q^{63} + 16q^{65} + 6q^{67} + 4q^{69} + 4q^{71} - 20q^{73} - 24q^{75} + 24q^{77} + 4q^{79} + 6q^{81} + 14q^{83} + 20q^{85} + 28q^{87} + 12q^{89} - 36q^{91} + 28q^{93} - 8q^{95} - 12q^{97} + 14q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(184))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 23
184.2.a.a \(1\) \(1.469\) \(\Q\) None \(0\) \(-1\) \(-4\) \(2\) \(-\) \(-\) \(q-q^{3}-4q^{5}+2q^{7}-2q^{9}-4q^{11}+\cdots\)
184.2.a.b \(1\) \(1.469\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-4\) \(+\) \(+\) \(q-q^{3}-2q^{5}-4q^{7}-2q^{9}-2q^{11}+\cdots\)
184.2.a.c \(1\) \(1.469\) \(\Q\) None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(q+4q^{7}-3q^{9}+6q^{11}-2q^{13}+6q^{17}+\cdots\)
184.2.a.d \(1\) \(1.469\) \(\Q\) None \(0\) \(3\) \(0\) \(-2\) \(+\) \(-\) \(q+3q^{3}-2q^{7}+6q^{9}-5q^{13}-6q^{17}+\cdots\)
184.2.a.e \(2\) \(1.469\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(4\) \(0\) \(-\) \(+\) \(q-\beta q^{3}+2q^{5}+(1+\beta )q^{9}+2\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(184))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(184)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 2}\)