Properties

Label 348.2.a
Level $348$
Weight $2$
Character orbit 348.a
Rep. character $\chi_{348}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $4$
Sturm bound $120$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 348 = 2^{2} \cdot 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 348.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(348))\).

Total New Old
Modular forms 66 4 62
Cusp forms 55 4 51
Eisenstein series 11 0 11

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

\(2\)\(3\)\(29\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(2\)

Trace form

\( 4q - 4q^{5} - 4q^{7} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{5} - 4q^{7} + 4q^{9} - 4q^{13} - 8q^{17} + 8q^{19} + 4q^{23} + 4q^{25} - 8q^{31} + 12q^{35} + 8q^{37} - 8q^{39} + 8q^{41} - 8q^{43} - 4q^{45} + 16q^{47} - 8q^{49} - 8q^{51} - 12q^{53} + 4q^{57} - 16q^{61} - 4q^{63} - 4q^{65} - 4q^{67} + 4q^{71} + 16q^{73} + 16q^{75} + 16q^{77} + 4q^{81} - 32q^{83} + 16q^{85} + 8q^{89} + 20q^{91} - 4q^{93} - 24q^{95} - 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(348))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 29
348.2.a.a \(1\) \(2.779\) \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) \(-\) \(+\) \(+\) \(q-q^{3}-2q^{5}+q^{7}+q^{9}+3q^{11}+5q^{13}+\cdots\)
348.2.a.b \(1\) \(2.779\) \(\Q\) None \(0\) \(-1\) \(0\) \(-3\) \(-\) \(+\) \(-\) \(q-q^{3}-3q^{7}+q^{9}-3q^{11}-3q^{13}+\cdots\)
348.2.a.c \(1\) \(2.779\) \(\Q\) None \(0\) \(1\) \(-4\) \(-3\) \(-\) \(-\) \(+\) \(q+q^{3}-4q^{5}-3q^{7}+q^{9}-q^{11}-3q^{13}+\cdots\)
348.2.a.d \(1\) \(2.779\) \(\Q\) None \(0\) \(1\) \(2\) \(1\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+q^{7}+q^{9}+q^{11}-3q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(348))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(348)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(174))\)\(^{\oplus 2}\)